tag:blogger.com,1999:blog-57358572668326105392024-03-05T00:47:41.385-08:00Bangkitkan SemangatFithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.comBlogger196125tag:blogger.com,1999:blog-5735857266832610539.post-90247029886376980562015-09-01T01:58:00.001-07:002015-09-01T02:04:30.484-07:00Setiap Orang Punya Rezekinya Masing-masingKamu percaya kalau setiap manusia punya rezekinya masing-masing?<br />
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Meski berungkap bahwa percaya, tetapi percaya tidak percaya rasanya masih aja ragu berbagi karena kebutuhan sendiri terhitung banyak, sedang penghasilan ngepas sana sini. Hayo nyakuuu, suka mikir gitu? hehe</div>
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Pernah nemuin kasus laki-laki berpikir lama untuk menikah lantaran belum punya banyak uang? Belum punya uang buat beli mobil pajero, belum punya uang buat beli rumah gedong, belum punya uang buat ngadain resepsi yang super duper mewar kayak orang-orang indonesia keneh.</div>
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Atau kasusnya BETI (Beda Tipis), kenapa BETI? Misal begini, dia udh siap mau nikah, eh kaka perempuannya ngelarang, "Punya uang berapa banyak lo mau ngelangkahin gue nikah? yang ngasih nafkah ke lo dari kecil siapa? lo yang gw besarin. Berani ngelangkahin gw? Rumah aja lo blm punya, mau berani-berani minta nikah duluan." wah ampun deh kasian banget tuh adik yah, cup cup yang sabar yaaah. </div>
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Atau atau kasus sang anak udah punya niatan nikah muda, belum juga sang anak minta restu, tapi udh keduluan diginiin, "Lee, jangan buru-buru nikah, bahagiain orang tua dulu, naik hajiin emak dulu, nunggu si sulung nikah dulu." </div>
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My God, kenapa orang indonesia begini. atau bukan org Indonesia deh apa yaaah haha. </div>
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Duh masih besarkah momok kekhawatiran kalau laki2 beristri akan sulit banyak berbagi terhadap keluarganya lantaran dinilai setelah punya istri dan anak maka penghasilannya akan lebih terfokus pada anak dan istrinya?</div>
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Coba saja orang-orang kita mengerti bahwa rezeki manusia sudah ada yang mengatur, rezeki gak akan pernah ketuker dengan yang lain atau di perjualbelikan misalnya.</div>
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Penulis sebagai wanita jadi ikutan riskan sama momok yang jadi panutan orang-orang baheula. </div>
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Gak semua perempuan begitu, gak semua perempuan bersikap protex penghasilan suaminya untuk di bagi-bagi.</div>
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Jadi keinget ceramah mama dedeh yang tema judulnya "Nikah dulu atau mapan dulu?"<br />
Semakin yakin kalau nikah gak mesti nunggu mapan:) </div>
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Manusia dengan rezeki yang dituliskan dengan cara "sampainya" yang beragam. </div>
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Untuk yang dikasih kesempatan diberi nikmat dengan harta yang berlimpah, berbahagialah karna kamu diberi hak istimewa oleh Allah untuk menjadi tangan-tangan Allah menyalurkan rizki orang-orang disekitarmu. Pernahkan kamu berfikir bahwa hartamu seutuhnya bukan milikmu? Harta adalah titipan, kamu bukan pemiliknya. Hindari seorang hartawan yang memanjakan diri sendiri.<br />
Banyak rezeki manusia bertebaran dimana-mana, berbahagialan menjadi tangan-tangan penyalur rezeki dari Allah. </div>
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Karena semua rezeki bisa di dapat bukan dari jalan yang hanya bisa di duga oleh akal manusia. </div>
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Selamat berbagi manusia pemilik hak istimewa.</div>
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Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-13165033304810247882014-08-16T17:37:00.001-07:002014-08-16T17:37:28.795-07:00Do'aTidak ada satu doapun yg sia-sia.<br />
Kamu percaya? Do'a akan kembali pada pemiliknya.<br />
Berdo'alah sebanyak mungkin.<br />
Jika dirasa doa tak kunjung ada balasan, bersabarlah<br />
Mungkin memang ada waktu yg tepat dimana doamu terjawabFithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com3tag:blogger.com,1999:blog-5735857266832610539.post-45918894858295449372014-07-06T05:46:00.000-07:002014-07-06T05:46:04.162-07:00Matahari, bumi.Mencintai itu suci. <div>
Memang banyak pilihan jalannya. Ada yang memang baik ada yg memang kurang baik caranya. </div>
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kadang kamu harus meneladani matahari, ia cinta pada bumi, tapi ia mengerti mendekat pada bumi justru membinasakan.</div>
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ah ya, masih tetap meneladani matahari terhadap bumi. Meski tak bisa dekat tapi juga tak bisa pergi:) Bumi bisa merasakan hangatnya sinat dari matahari dan matahari ridho menghangatkan bumi. </div>
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Ada cinta yang tak bisa dibahasakan.</div>
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Allah benar-benar romantis:')</div>
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Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com2tag:blogger.com,1999:blog-5735857266832610539.post-69123680820831842222014-06-23T23:05:00.000-07:002014-07-06T05:35:56.380-07:00Anak butuh di percaya, di jaga rahasianya. Ketika anak bercerita banyak dan percaya bahwa akan di jaga rahasianya,<br />
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saat itu seorang anak benar-benar percaya bahwa dia akan sangat merasa aman dan nyaman.<br />
Anak akan terus banyak bercerita, tentang dirinya,tentang perasaannya, tentang hal baru yang ia pelajari, dan tidak menutup kemungkinan untuk bercerita yg masih berbau privasi.</div>
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Anak butuh di jaga rahasianya, dengan begitu dia akan terus percaya. Dia akan terus terbuka, tidak lagi meragukan banyak hal. </div>
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Tetapi jika kepercayaannya tidak dijaga, maka jangan salahkan jika ia enggan untuk bercerita dengan leluasa seperti sedia kala, jangan salahkan jika anak lebih memilih diam, lebih memilih untuk sendiri menutupi masalahnya. lebih memilih untuk tidak berbagi.<br />
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Anak butuh dipercaya, dijaga rahasianya. </div>
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#pelajaran hari ini | next time berjuang untuk jadi ibu tauladan | training</div>
Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com2tag:blogger.com,1999:blog-5735857266832610539.post-81878645111287215562014-02-20T19:34:00.002-08:002014-02-20T19:34:11.072-08:00gk jelaslama rasanya sudah tidak menulis disini.. <div>
aku punya banyak cerita. banyak yang tersimpan namun rasanya tidak bisa semuanya diceritakan disini. #apa deh yaaa ==a</div>
Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-56692959474105498782013-12-12T08:29:00.000-08:002013-12-12T08:31:43.535-08:00Amalan Nabi Daud a.sSudah lama sekali rasanya gak banyak omong disini.<br />
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dan alhamdulillah punya jengukin ikan-ikan mungkin dan keluarga pinguin yang harmonis. yeeeeh :D</div>
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Ini berbicara soal amalannya Nabi Daud a.s </div>
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Sebagai muslim pasti taulah kisahnya Nabi Daud a.s</div>
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Pernah denger dong soal <i><b><span style="background-color: black; color: magenta;">puasa daud</span></b></i></div>
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<span style="background-color: black;">Puasa Daud itu amalannya nabi daud, berpuasa selang-seling. Sehari puasa dan sehari tidak, begitu seterusnya.</span></div>
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<span style="background-color: black;">Kedengerannya berat buat ikutan ngejalaninnya. Sadar tidak sadar, manusia itu punya berbagai alasan krn punya banyak perhitungan. Tidak ada yg salah dengan kodrat ini karena kita di bebaskan untuk memilih jalannya masing-masing ..</span></div>
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<span style="background-color: black;">Rasulullah SAW sangat suka dengan amalan nabi daud ini, namun beliu tidak mengamalkannya dikarenakan khawatir menyulitkan umatnya. Mengapa dirasa menyulitkan? Hey, ingat.. bahwa beliau adalah teladan kita. umatnya yang begitu banyak akan mencontoh dan mengamalkan apa yang Rasulullah lakukan. dan Subhanallahnya, Rasul kita itu tau bagaimana perkiraan keadaan umatnya. Maka Rasulullah memilih untuk rutin melaksanakan puasa senin-kamisnya. Bagi yang cinta dengan Rasul kita ini :) YUK amalkan Puasa senin-kamisnya :'D</span></div>
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<span style="background-color: black;">bersambung ..</span></div>
Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-78217381840287147042013-11-25T18:46:00.001-08:002013-11-25T18:51:23.426-08:00MR<a href="http://asarohqi.blogspot.com/2012/03/pembelajaran-matematika-dengan.html">Matematika Realistik</a> <a href="http://faizalnizbah.blogspot.com/2013/05/pengertian-pendekatan-matematika.html">></a><br />
<br />Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-37139721483135122502013-11-24T06:44:00.000-08:002013-11-24T06:45:23.964-08:00Menghadirkan Kamu<div style="color: #444444; font-family: 'Helvetica Neue', HelveticaNeue, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;">
Sadar tidak sadar. Doa rutin setelah mendoakan orgtua adalah..</div>
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<strong><em>Ya Allah baguskan akhlakku,</em> baguskan<em> akhlak pasanganku</em></strong></div>
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Aku percaya, mungkin karena doa itu Allah jadi banyak berbicara kepadaku, menyampaikan ilmu yang harus aku tau, yang mesti aku pelajari dan yang harus aku lalui kenikmatan prosesnya. </div>
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Terimakasih untuk segalanya wahai kekasih hati:) aku sadar perlahan Allah meniupkan kekuatan di balik setiap kejadian. agar menjadi pribadi yang teguh, pribadi yang memaafkan, yang lembut lagi sabar. Maka baguskan akhlaku ya Allah..</div>
Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-24635765296389441822013-11-23T06:54:00.001-08:002013-11-23T06:58:58.073-08:00Emas dan Kamu:)<div style="color: #444444; font-family: 'Helvetica Neue', HelveticaNeue, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;">
Tentang sebuah tekat dan niat suci..<br />
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Selalu teringat untuk bisa selalu sabar tanpa batas.</div>
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katamu, 'Ingatlah intan yang terbentuk dari banyak tekanan dan suhu yang tinggi."</div>
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lalu kau torehkan emas.<br />
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<blockquote class="tr_bq">
<strong><em>'Hey, emas itu jarang ditemukan. Dari 1 ton bijih kandungan emasnya hanya 1 gram. Kamu tau artinya apa? Artinya dari 1 juta orang, yang punya karakteristik seperti emas hanya ada satu. Karakteristik emas itu stabil, gak mudah terpengaruh oleh lingkungan. Jadi kesimpulannya orang yang punya pendirian teguh berarti mirip seperti emas.'</em></strong></blockquote>
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Terimakasih sudah menginspirasi:)</div>
Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-79203109174041017062013-10-03T18:41:00.003-07:002013-10-03T18:41:26.543-07:00Dibalik peristiwa<span style="background-color: white; color: #37404e; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; line-height: 17.99715805053711px;">Allah punya rencana indah di balik semua peristiwa </span><i class="_4-k1 img sp_2a7397 sx_29d9ed" style="background-color: white; background-image: url(https://fbstatic-a.akamaihd.net/rsrc.php/v2/yc/r/ERwAtiRKR7Q.png); background-position: -43px -697px; background-repeat: no-repeat no-repeat; background-size: auto; color: #37404e; display: inline-block; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; height: 16px; line-height: 17.99715805053711px; vertical-align: -3px; width: 16px;"></i><span style="background-color: white; color: #37404e; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; line-height: 17.99715805053711px;"> </span><br />
<span style="background-color: white; color: #37404e; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; line-height: 17.99715805053711px;">terlepas dari peristiwa yang kita sebut dengan buruk ataupun baik.</span><br style="background-color: white; color: #37404e; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; line-height: 17.99715805053711px;" /><span style="background-color: white; color: #37404e; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; line-height: 17.99715805053711px;">Jika sesuatu yang kita harapkan atau yang kita inginkan itu tiba-tiba saja di ambil,</span><br />
<span style="background-color: white; color: #37404e; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; line-height: 17.99715805053711px;">lantas kita bisa seenaknya merengek bahwa Allah tidak adil?</span><br />
<span style="background-color: white; color: #37404e; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; line-height: 17.99715805053711px;">kemudian meronta-ronta bahwa Allah itu tega? begitukah? Bukan begitu sayang </span><i class="_4-k1 img sp_2a7397 sx_29d9ed" style="background-color: white; background-image: url(https://fbstatic-a.akamaihd.net/rsrc.php/v2/yc/r/ERwAtiRKR7Q.png); background-position: -43px -697px; background-repeat: no-repeat no-repeat; background-size: auto; color: #37404e; display: inline-block; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; height: 16px; line-height: 17.99715805053711px; vertical-align: -3px; width: 16px;"></i><br style="background-color: white; color: #37404e; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; line-height: 17.99715805053711px;" /><span style="background-color: white; color: #37404e; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; line-height: 17.99715805053711px;"><br /></span><br />
<span style="background-color: white; color: #37404e; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; line-height: 17.99715805053711px;">Allah mau liat <i>action</i> kita, Allah mau lihat hamba kesayangannya itu. </span><br />
<span style="background-color: white; color: #37404e; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; line-height: 17.99715805053711px;">Tetaplah menjadi pribadi yang selalu memperbaiki diri:) </span><br />
<span style="background-color: white; color: #37404e; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; line-height: 17.99715805053711px;">patrikan dalam diri bahwa masih banyak kekurangan, </span><br />
<span style="background-color: white; color: #37404e; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; line-height: 17.99715805053711px;">patrikan dalam hati bahwa masih perlu banyak belajar. </span><br />
<span style="background-color: white; color: #37404e; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; line-height: 17.99715805053711px;">Agar senantiasa tidak merasa puas untuk selalu muhasabah diri^_^</span><br style="background-color: white; color: #37404e; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; line-height: 17.99715805053711px;" /><br style="background-color: white; color: #37404e; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; line-height: 17.99715805053711px;" /><span style="background-color: white; color: #37404e; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 12.727272033691406px; line-height: 17.99715805053711px;">"Dan karena Tuhanmu, Bersabarlah." (QS. Al-Muddassir :7)</span>Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-66022334599341370172013-08-19T18:33:00.000-07:002013-08-19T18:33:08.900-07:00Resep Nasi Goreng terlur isi tempe<div class="separator" style="clear: both; text-align: center;">
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<br />Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-39658479258199441592013-08-11T23:45:00.001-07:002013-08-19T17:31:00.694-07:00Resep Memasak CumiOke guys, what are you doing now? bagi yang nganggur dari pada bingung2 enaknya mau ngapain. Atau bagi yang laper tapi bingung mau makan apa, mending ikutin resep ini aja nih, kita masak cumi ala aku, hahahah<br />
oke, le'ts try together me! Are you Ready? :D<br />
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Bahan :<br />
1/4kg Cumi. Buang kantung tintanya, cuci bersih dan potong-potong<br />
2 lembar daun pandan<br />
1/2 biji cabe rawit merah<br />
2 sdt gula merah<br />
1 buah jeruk nipis<br />
5 sdm saus tiram<br />
1/2 garam<br />
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Bahan untuk membuat bumbu :<br />
4 buah cabe<br />
4 butir bawang merah<br />
3 siung bawang putih<br />
1/2 sdt terasi<br />
1/4 cangkir air asam kental<br />
1/2 sdm merica bubuk<br />
<br />
Cara Memasak :<br />
<br />
<ol>
<li>Cumi terlebih dahulu di cuci bersih kemudian campurkan dengan air jeruk nipis, diamkan selama kurang lebih 30 menit agar cumi tidak amis.</li>
<li>Panaskan minyak, tumis bumbu halus hingga wangi</li>
<li>Masukkan cumi-cumi, daun pandan, cabe rawit, & garam, aduk sesekali</li>
<li>Masukan 1/4 cangkir air asam kental (air rendaman asam)\</li>
<li>Masukan gula merah, aduk rata</li>
<li>Masak hingga 5 menit lalu masukkan gula merah & saus tiram. aduk rata</li>
<li>Angkat dan sajikan untuk keluarga tercinta. Selamat mencoba :D</li>
</ol>
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<br /></div>
<div>
Bingung mesti ngasih nama cumi apa, jadiiii terserah deh yaaah, cobain aja buat bikin sendiri di rumah, dan rasakan nikmatnya hehe ;)</div>
<div>
Semoga bermanfaat bagi yang sedang belajar masak, atau sengaja mencoba resep baru untuk keluarga di rumah... </div>
<div>
Masak? </div>
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KATAKAN</div>
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It's enjoyeble of me !</div>
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Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com2tag:blogger.com,1999:blog-5735857266832610539.post-89470891993994255562013-08-04T17:59:00.000-07:002013-08-14T18:17:38.151-07:00Bukber SAPELA di Ramadhan tahun 2013 M<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJTQCnOfaHuXyJu-rIdwGfT6mRt3YvRK42kIHczDRLeaQZG5IRkdY6b_p2fYKRanQToEgGrzrh3GT1JO8IqxYPP-EZTY5JdstXm1SiS_KVf6fUC290LurN9ICCW_LQaLMRKTqItcbQH1s/s1600/C360_2013-08-05-01-08-42_org.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJTQCnOfaHuXyJu-rIdwGfT6mRt3YvRK42kIHczDRLeaQZG5IRkdY6b_p2fYKRanQToEgGrzrh3GT1JO8IqxYPP-EZTY5JdstXm1SiS_KVf6fUC290LurN9ICCW_LQaLMRKTqItcbQH1s/s320/C360_2013-08-05-01-08-42_org.jpg" width="320" /></a></div>
<br />
Tentu kehendak Allah yang menjadikan kami bersaudara, hingga sepakat dihati masing-masing bahwa kami keluarga.<br />
<div>
Ya Allah, ini sungguh luar biasa untukku..</div>
<div>
Terimakasih atas karuniaMu ya Allah, memberi apa yang sekiranya aku butuhkan, yah.. mereka sangat aku butuhkan, butuh dalam konteks apa? aku rasa, untuk jiwa, rasanya jiwa ini sedikitnya ternafkahi dengan adanya mereka di perjalanan hidupku ini :) Setelah Engkau beri aku keluarga yang sangat harmonis, saudara satu keturunan yang begitu sangat mencinta, Engkaupun tak habis-habisnya menghendaki aku untuk memiliki mereka, keluarga Saung Pelangi.</div>
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Tanggal 3 Agustus 2013, </div>
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di kediaman Neneng Maulida. Cilegon-Banten.</div>
<div>
Meski gak semua keluarga sapela bisa kumpul, 5 diantaranya berhalangan untuk hadir.</div>
<div>
Alhamdulillah bisa bersilaturahmi dengan keluarga neneng disana, banyak yg aku baru tau soal neneng adikku ini, yah aku mengganggapnya sebagai adik, dia manis menurutku, senyumnya itu loh, masya Allah manis sekali. Gak ada alasan yang membuatku untuk tidak sayang padanya:)</div>
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<br /></div>
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Sebulan lamanya kami KKM di desa masing-masing, terpencae-pencar. </div>
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Dengan acara buka bersama di kediaman Neneng ini, kami melepas rindu dengan banyak bercerita soal pengalaman di lokasi KKM masing-masing. </div>
<div>
Tuker kado, foto bersama. yah mungkin suatu saat nanti, aku akan sangat merindukan saat-saat bersama dengan mereka. Harapku semoga tali persaudaraan dan silaturahmi kami senantiasa terjaga, sampai nenek kakek, bahkan hingga ajal menjemput. Semoga akan banyak doa yang terbang untuk setiap kami, karena bagiku, media doa yang bisa menjamin bahwa kita akan terus bersatu:) karena bukan ikatan darah yang menyebabkan kita menjadi saudara bahkan keluarga, tapi ikatan hati melalu doa, yah dari situlah kami menjadi bersaudara:) </div>
<div>
<br /></div>
<div>
Allah, Ya Latief, sampaikanlah pada hati-hati mereka, bahwa aku sangat sayang mereka :') dengan caraku yang mungkin tidak sampai untuk menyentuh hati-hatinya, dengan caranku yang mungkin cuek dengan setiap masalah mereka, dengan caraku yang mungkin terkadang kesannya terlalu ramai untuk bicara, maka ku mohon, hanya Engkau yang mampu untuk menyampaikan ini, aku... Aku sayang mereka karena Engkau Ya Allah, Selamatkan mereka di dunia ini, selamatkan mereka di akhirat kelak ;') Aamiin</div>
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Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-83114106322214538922013-08-04T16:47:00.000-07:002013-08-04T16:47:34.836-07:00Udah lama gak jengukinaaaaaaaaaaaaaaaaaagh, maaf ya blog udh lama gak jengukin kamu, jadi bersarang laba-laba gini deh yaah..<div>
Ikan-ikan jadi mandiri banget gak aku kasih makan, hehe</div>
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Jadi kangen rasanya :D</div>
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<br /></div>
<div>
Meski gak nulis di sini aku, aku sempet coret2 di Tumblr loh, </div>
<div>
ini dia, <a href="http://fifisayangmamah.tumblr.com/">Tumblr aku, klik ini silahkan</a></div>
Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-54867350603935351152013-05-21T00:48:00.000-07:002013-05-21T00:48:22.523-07:00Areas under the Normal Curve<br />
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">The curve of any continuous
probability distribution or density function is constructed so that the area
under the curve bounded by the two ordinatos <i>x — x\</i> and <i>x — x</i></span><i><span style="font-family: "Times New Roman","serif"; font-size: 6.5pt;">2 </span></i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">equals the
probability that the random variable <i>X </i>assumes a value between <i>x </i>=
<i>x\ </i>and <i>x </i>= <i>x</i></span><i><span style="font-family: "Times New Roman","serif"; font-size: 6.5pt;">2</span></i><i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">. </span></i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">Thus, for the
normal curve in Figure 6.6,<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">In Figures 6.3, 6.4, and 6.5 we
saw how the normal curve is dependent on the mean and the standard deviation of
the distribution under investigation. The area under the curve between any two
ordinates must then also depend on the values <i>p</i> and <i>a. </i>This is
evident in Figure 6.7, where we have shaded regions corresponding<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">to <i>P(xi < X < x-2) </i>for
two curves with different means and variances. The <i>P{x\ < X < x</i></span><i><span style="font-family: "Times New Roman","serif"; font-size: 6.5pt;">2</span></i><i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">), </span></i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">where <i>X </i>is
the random variable describing distribution A, is indicated<i> </i>by the
darker shaded area. If <i>X </i>is the random variable describing distribution <i>B,
</i>then <i>P(x.\ < X < x</i></span><i><span style="font-family: "Times New Roman","serif"; font-size: 6.5pt;">2</span></i><i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">) </span></i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">is given by the
entire shaded region. Obviously, the two<i><o:p></o:p></i></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">shaded regions are different in size;
therefore, the probability associated with each distribution will be different
for the two given values <i>ol X.</i> The difficulty encountered in solving
integrals of normal density functions necessitates the tabulation of normal
curve areas for quick reference. However, it </span></div>
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</div>
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<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;"><span style="color: purple;"><b>Definition</b></span><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">The distribution of a normal
random variable with mean 0 and variance 1 is called<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">a <b>standard normal
distribution.<o:p></o:p></b></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">The original and transformed
distributions are illustrated in Figure 6.8. Since<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">all the values of <i>X </i>falling
between <i>x\ </i>and <i>x</i></span><i><span style="font-family: "Times New Roman","serif"; font-size: 6.5pt;">2 </span></i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">have corresponding <i>z </i>values
between<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">z\ </span></i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">and <i>z</i></span><i><span style="font-family: "Times New Roman","serif"; font-size: 6.5pt;">2</span></i><i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">, </span></i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">the area under
the <i>X-curve </i>between the ordinates <i>x = x\ </i>and <i>x = x</i></span><i><span style="font-family: "Times New Roman","serif"; font-size: 6.5pt;">2 </span></i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">in<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">Figure 6.8 equals the area under
the Z-curve between the transformed ordinates<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">z </span></i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">= <i>z\ </i>and <i>z
— z</i></span><i><span style="font-family: "Times New Roman","serif"; font-size: 6.5pt;">2</span></i><i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">.<o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">We have now reduced the required
number of tables of normal-curve areas to<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">one, that of the standard normal
distribution. Table A.3 indicates the area under<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">the standard normal curve
corresponding to <i>P(Z < z) </i>for values of <i>z </i>ranging from<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">—3.49 to 3.49. To illustrate the
use of this table, let us find the probability that <i>Z<o:p></o:p></i></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">is less than 1.74. First, we
locate a value of <i>z </i>equal to 1.7 in the left column, then<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">move across the row to the column
under 0.04, where we read 0.9591. Therefore,<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">P(Z < </span></i><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">1.74) = 0.9591.
To find a <i>z </i>value corresponding to a given probability, the<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">process is reversed. For example,
the <i>z </i>value leaving an area of 0.2148 under the<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;">curve to the left of <i>z </i>is
seen to be —0.79</span></div>
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Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-36910597457799687422013-05-20T17:59:00.000-07:002013-05-20T17:59:43.831-07:00Sebaran Seragam Kontinu<br />
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">One of the simplest continuous
distributions in all of statistics is the <b>continuous<o:p></o:p></b></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">uniform
distribution. </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">This
distribution is characterized by a density function<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">that is "flat," and
thus the probability is uniform in a closed interval, say [A, <i>B].<o:p></o:p></i></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Although applications of the
continuous uniform distribution are not as abundant<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">as they are for other distributions
discussed in this chapter, it is appropriate for<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">the novice to begin this
introduction to continuous distributions with the uniform<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">distribution.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Uniform Distribution<o:p></o:p></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikxSnjPHsO54DHG3p5qfsr2S8hO228g6_py1lSHuDMK0ta56zr6KK1sZpwIS-BIhI8iFgG36-EXzgQ9ox9zHG6RMhfYGvAh5mlAEUQBEt9zdOXe7sOsgAvHrzRN54T-iezayqGYHZhyBo/s1600/hi.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="106" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikxSnjPHsO54DHG3p5qfsr2S8hO228g6_py1lSHuDMK0ta56zr6KK1sZpwIS-BIhI8iFgG36-EXzgQ9ox9zHG6RMhfYGvAh5mlAEUQBEt9zdOXe7sOsgAvHrzRN54T-iezayqGYHZhyBo/s320/hi.png" width="320" /></a></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">It should be emphasized to the
reader that the density function forms a rectangle<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">with base <i>B — A </i>and <b>constant
height </b><i>-g^j- </i>As a result, the uniform distribution<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">is often called the <b>rectangular
distribution. </b>The density function for a uniform<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">random variable on the interval
[1, 3] is shown in Figure 6.1.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Probabilities are simple to
calculate for the uniform distribution due to the<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">simple nature of the density
function. However, note that the application of this<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">distribution is based on the
assumption that the probability of falling in an interval<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">of fixed length within [A, <i>B] </i>is constant.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Example :<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Suppose that a large conference
room for a certain company can be reserved for no<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">more than 4 hours. However, the
use of the conference room is such that both long<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">and short conferences occur quite
often. In fact, it can be assumed that length <i>X<o:p></o:p></i></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">of a conference has a uniform
distribution on the interval [0, 4].<o:p></o:p></span></div>
<div class="MsoListParagraph" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">( (a)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">What
is the probability density function?</span></div>
<div class="MsoListParagraphCxSpLast" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaBcPFxl2vbeKFL9B1f5NnVvCGFeVfXHrlgP5XxKV60w68A5L5Cf-AR1oieypNWf-Fg7dCi1uiX8Ht67QJkowEg5SyUzBPqjaF7xu6BG4f58M9_J9BBP1PI1OnHGC-lS_7C30Ovl8c9kU/s1600/g.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="168" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaBcPFxl2vbeKFL9B1f5NnVvCGFeVfXHrlgP5XxKV60w68A5L5Cf-AR1oieypNWf-Fg7dCi1uiX8Ht67QJkowEg5SyUzBPqjaF7xu6BG4f58M9_J9BBP1PI1OnHGC-lS_7C30Ovl8c9kU/s320/g.png" width="320" /></a> </div>
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<span style="font-size: 12pt; text-align: start; text-indent: -24px;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<span style="font-size: 12pt; text-align: start; text-indent: -24px;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<span style="font-size: 12pt; text-align: start; text-indent: -24px;">(b)<span style="font-size: 7pt;"> </span></span><span style="font-size: 12pt; text-align: start; text-indent: -24px;">What is the probability that any given conference lasts at least 3 hours?</span></div>
<br />
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Solution: </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">(a) The
appropriate density function for the uniformly distributed random variable<o:p></o:p></span></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">X </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">in this
situation is <o:p></o:p></span></div>
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<br /></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0sfkZgF9XAusL2i0-4gtgkVZgWPeJx3MA9ARdDSIKu8v1D2ZG_NT34DYIaGq5vJks5LP2gmYR6ZnhW8E95PKONJEaO9aoIGZ1TM8_jiarCm2gDpnHNMmRDQ5_yXc-egpcoGSIXylRh18/s1600/hj.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="165" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0sfkZgF9XAusL2i0-4gtgkVZgWPeJx3MA9ARdDSIKu8v1D2ZG_NT34DYIaGq5vJks5LP2gmYR6ZnhW8E95PKONJEaO9aoIGZ1TM8_jiarCm2gDpnHNMmRDQ5_yXc-egpcoGSIXylRh18/s320/hj.png" width="320" /></a></div>
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<br /></div>
Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-60769685283125070932013-05-19T22:20:00.001-07:002013-05-19T22:20:19.657-07:00Sebaran Poisson<br />
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Experiments
yielding numerical values of a random variable <i>X, </i>the number of<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">outcomes
occurring during a given time interval or in a specified region, are called<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Poisson
experiments. </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">The
given time interval may be of any length, such as<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">a minute, a day,
a week, a month, or even a year. Hence a Poisson experiment<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">can generate
observations for the random variable X representing the number of<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">telephone calls
per hour received by an office, the number of days school is closed<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">due to snow
during the winter, or the number of postponed games due to rain<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">during a
baseball season. The specified region could be a line segment, an area,<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">a volume, or
perhaps a piece of material. In such instances <i>X </i>might represent<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">the number of
field mice per acre, the number of bacteria in a given culture, or<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">the number of
typing errors per page. A Poisson experiment is derived from the<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Poisson process </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">and
possesses the following properties:<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Properties of
Poisson Process<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">1. The number of
outcomes occurring in one time interval or specified region is<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">independent of
the number that occurs in any other disjoint time interval or<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">region of space. In
this way wc say that the Poisson process has no memory.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">2. </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">The probability
that a single outcome will occur during a very short time<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">interval or in a
small region is proportional to the length of the time interval<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">or the size of
the region and does not depend on the number of outcomes<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">occurring
outside this time interval or region.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">3. The
probability that more than one outcome will occur in such a short time<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">interval or fall
in such a small region is negligible.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">The number X of
outcomes occurring during a Poisson experiment is called a<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Poisson random
variable, </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">and
its probability distribution is called the <b>Poisson<o:p></o:p></b></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">distribution. </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">The mean number
of outcomes is computed from <i>p </i>= <i>Xt, </i>where<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">t </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">is the specific
"time," "distance," "area," or "volume"
of interest. Since its<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">probabilities
depend on A, the rate of occurrence of outcomes, we shall denote<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">them by the
symbol <i>p(x; Xt). </i>The derivation of the formula for <i>p(x; Xt), </i>based
on<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">the three
properties of a Poisson process listed above, is beyond the scope of this<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">book. The following
concept is used for computing Poisson probabilities.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Poisson
Distribution<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">The probability
distribution of the Poisson random variable X, representing<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">the number of
outcomes occurring in a given time interval or specified region<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">denoted
by <i>t, </i>is </span><span style="color: #333333; font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: IN;">P(<i>x</i>;λt) = <!--[if gte vml 1]><v:shapetype
id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
<v:stroke joinstyle="miter"/>
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0"/>
<v:f eqn="sum @0 1 0"/>
<v:f eqn="sum 0 0 @1"/>
<v:f eqn="prod @2 1 2"/>
<v:f eqn="prod @3 21600 pixelWidth"/>
<v:f eqn="prod @3 21600 pixelHeight"/>
<v:f eqn="sum @0 0 1"/>
<v:f eqn="prod @6 1 2"/>
<v:f eqn="prod @7 21600 pixelWidth"/>
<v:f eqn="sum @8 21600 0"/>
<v:f eqn="prod @7 21600 pixelHeight"/>
<v:f eqn="sum @10 21600 0"/>
</v:formulas>
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
<o:lock v:ext="edit" aspectratio="t"/>
</v:shapetype><v:shape id="Picture_x0020_4" o:spid="_x0000_i1028" type="#_x0000_t75"
alt="Description: http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302621/latex-e6db8c52308b69af7848d3d41626e477.png"
style='width:69pt;height:19.5pt;visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png"
o:title="latex-e6db8c52308b69af7848d3d41626e477"/>
</v:shape><![endif]--><!--[if !vml]--><img alt="Description: http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302621/latex-e6db8c52308b69af7848d3d41626e477.png" height="26" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png" v:shapes="Picture_x0020_4" width="92" /><!--[endif]--> , <i>x</i> =
0, 1, 2, ...<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="color: #333333; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: IN;">where A is the average
number of outcomes per unit time, distance, area, or volume, and e=2.71828<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">for a few
selected values of At ranging from 0.1 to 18. We illustrate the use of this<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">table with the
following two examples.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">During a
laboratory experiment the average number of radioactive particles passing<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">through a
counter in 1 millisecond is 4. What is the probability that 6 particles<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">enter the
counter in a given millisecond?<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Solution: </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Using
the Poisson distribution with <i>x </i>= 6 and <i>Xt </i>= 4 and Table A.2, we
have<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 12.0pt; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;">
<span style="color: #333333; font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: IN;">P(6,4) =<!--[if gte vml 1]><v:shape
id="Picture_x0020_3" o:spid="_x0000_i1027" type="#_x0000_t75" alt="Description: http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302621/latex-d9207beead2e18b8433723aed080b769.png"
style='width:42.75pt;height:22.5pt;visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image002.png"
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</v:shape><![endif]--><!--[if !vml]--><img alt="Description: http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302621/latex-d9207beead2e18b8433723aed080b769.png" height="30" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image002.png" v:shapes="Picture_x0020_3" width="57" /><!--[endif]--> = <!--[if gte vml 1]><v:shape id="Picture_x0020_2"
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</v:shape><![endif]--><!--[if !vml]--><img alt="Description: http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302621/latex-cb844eff6efa2c605cb6a87dba34edaa.png" height="22" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image004.png" v:shapes="Picture_x0020_1" width="90" /><!--[endif]--> <o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 12.0pt; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;">
<span style="color: #333333; font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: IN;">
= 0.8893 – 0.7851<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 12.0pt; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;">
<span style="color: #333333; font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: IN;"> =
0.1042<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Example :<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Ten is the
average number of oil tankers arriving each day at a certain port city.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">The facilities
at the port can handle at most 15 tankers per day. What is the<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">probability that
on a given day tankers have to be turned away?<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 12.0pt; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;">
<b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Solution: </span></i></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Let X be the
number of tankers arriving each day. Then, using Table A.2, we have</span><span style="color: #333333; font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: IN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="color: #333333; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: IN;">P(X>15) = 1 – P(X=
1) = 0,0487<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Like the
binomial distribution, the Poisson distribution is used for quality control,<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">quality
assurance, and acceptance sampling. In addition, certain important<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">continuous
distributions used in reliability theory and queuing theory depend on<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">the Poisson
process. Some of these distributions arc discussed and developed in<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Chapter 6.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="color: #333333; font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: IN;"> Teorem<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Both
the mean and variance of the Poisson distribution <i>p(x; Xt) </i>are <i>Xt.<o:p></o:p></i></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">The proof of
this Theorem is found in Appendix A.26.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">In Example 5.20,
where <i>Xt — </i>4, we also have <i>a<sup>2</sup> — </i>4 and hence <i>a = </i>2.
Using<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Chebyshev's
theorem, we can state that our random variable has a probability of at<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">least 3/4 of
falling in the interval <i>p±2a </i>= 4± (2)(2), or from 0 to 8. Therefore, we<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">conclude that at
least three-fourths of the time the number of radioactive particles<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">entering
the counter will be anywhere from 0 to 8 during a given millisecond.</span><span style="color: #333333; font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: IN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">The Poisson
Distribution as a Limiting Form of the Binomial<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">It should be
evident from the three principles of the Poisson process that the<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Poisson
distribution relates to the binomial distribution. Although the Poisson<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">usually finds
applications in space and time problems as illustrated by Examples<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">5.20 and 5.21,
it can be viewed as a limiting form of the binomial distribution.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">In the case of
the binomial, if <i>n </i>is quite large and p is small, the conditions<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">begin to
simulate the <i>continuous space or time region </i>implications of the Poisson<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">process. The
independence among Bernoulli trials in the binomial case is consistent<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">with property 2
of the Poisson process. Allowing the parameter <i>p </i>to be close to<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">zero relates to
property 3 of the Poisson process. Indeed, if n is large and <i>p </i>is<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">close to 0, the
Poisson distribution can be used, with <i>p = np, </i>to approximate<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">binomial
probabilities. If <i>p </i>is close to 1, we can still use the Poisson distribution<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">to approximate
binomial probabilities by interchanging what we have defined to<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">be a success and a
failure, thereby changing <i>p </i>to a value close to 0.<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 12.0pt; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="background: white; line-height: 12.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: IN;">Teorem<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 12.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: IN;">Let X be a binomial random variable with probability distribution <i>b(x;n,p). </i>When <i>n </i>→∞, <i>p →</i> 0,
and η<i> </i>=n<i>p </i>remains constant, <i>b(x;n,p) —</i>>p(x;.µ).<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 12.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-40104994474976784142013-05-19T21:33:00.005-07:002013-05-19T21:36:37.153-07:00Hypergeometric Distribution<br />
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt; text-align: justify;">The simplest way
to view the distinction between the binomial distribution of Section 5.3 and the
hypergeometric distribution lies in the way the sampling is clone. The types of
applications of the hypergeometric arc very similar to those of the binomial
distribution. We are interested in computing probabilities for the number of
observations that fall into a particular category. But in the case of the binomial,
independence among trials is required. As a result, if the binomial is applied
to. say, sampling from a lot of items (deck of cards, batch of production items),
the sampling must be clone withreplacement of each item after it is observed.
On the other hand, flic hypergeometric distribution does not require independence
and is based on the: sampling done with outreplacement. Applications for the
hypergeometric distribution are found in many areas, with heavy uses in
acceptance sampling, electronic testing, and quality assurance. Obviously, for
many of these fields testing is done at the expense of the item being tested.
That is, the item is destroyed and hence cannot be replaced in the sample. Thus
sampling without replacement is necessary. A simple example: with playing cards
will serve as our first illustration. If we wish to find the: probability of
observing 3 red cards in 5 draws from an ordinary deck of 52 playing cards, the
binomial distribution of Section 5.3 does not apply unless each card is
replaced and the deck reshuffled before the next drawingis made. To solve the
problem of sampling without replacement, let. us restate the problem. If 5
cards are drawn at random, we are interested in the probability of selecting 3
red cards from the 26 available and 2 black cards from the 26 black cards available
in the deck. There are </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%; position: relative; text-align: justify; top: 10pt;"><v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f">
<v:stroke joinstyle="miter">
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0">
<v:f eqn="sum @0 1 0">
<v:f eqn="sum 0 0 @1">
<v:f eqn="prod @2 1 2">
<v:f eqn="prod @3 21600 pixelWidth">
<v:f eqn="prod @3 21600 pixelHeight">
<v:f eqn="sum @0 0 1">
<v:f eqn="prod @6 1 2">
<v:f eqn="prod @7 21600 pixelWidth">
<v:f eqn="sum @8 21600 0">
<v:f eqn="prod @7 21600 pixelHeight">
<v:f eqn="sum @10 21600 0">
</v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas>
<v:path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f">
<o:lock aspectratio="t" v:ext="edit">
</o:lock></v:path></v:stroke></v:shapetype><v:shape id="_x0000_i1025" style="height: 26.25pt; width: 27.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png">
</v:imagedata></v:shape></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; text-align: justify;"> ways of
selecting 3 red cards, and for each of these ways wc can choose 2 black cards
in </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%; position: relative; text-align: justify; top: 10pt;"><v:shape id="_x0000_i1025" style="height: 25.5pt; width: 27.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image002.png">
</v:imagedata></v:shape></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; text-align: justify;"> ways. Therefore, the total number of ways to
select 3 red and 2 black cards in 5 draws is the product </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%; position: relative; text-align: justify; top: 10pt;"><v:shape id="_x0000_i1025" style="height: 26.25pt; width: 57.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; text-align: justify;"> The total number of ways to select any 5 cards
from the 52 that are available is </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%; position: relative; text-align: justify; top: 10pt;"><v:shape id="_x0000_i1025" style="height: 26.25pt; width: 27.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image004.png">
</v:imagedata></v:shape></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; text-align: justify;"> . Hence the probability of selecting 5 cards
without replacement of which 3 are red and 2 are black is given by </span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
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style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>26</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>3</m:r></span></i></m:den></m:f></m:e></m:d><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
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m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
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style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>26</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>2</m:r></span></i></m:den></m:f></m:e></m:d></m:num><m:den><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
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m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>52</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>5</m:r></span></i></m:den></m:f></m:e></m:d></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>-</m:r><m:r>
</m:r></span></i><m:f><m:fPr><span style='font-size:16.0pt;mso-ansi-font-size:
16.0pt;mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:"Cambria Math";
mso-bidi-font-family:"Times New Roman";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:
16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman"'><m:r>26!</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman"'><m:r>3!23!</m:r></span></i></m:den></m:f></m:e></m:d><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:
16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman"'><m:r>26!</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman"'><m:r>2!24!</m:r></span></i></m:den></m:f></m:e></m:d></m:num><m:den><m:f><m:fPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman"'><m:r>52!</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman"'><m:r>5!47!</m:r></span></i></m:den></m:f></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;font-family:
"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:
minor-fareast;mso-bidi-font-family:"Times New Roman"'><m:r> </m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -19.5pt; position: relative; top: 19.5pt;"><v:shape id="_x0000_i1025" style="height: 46.5pt; width: 138.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image005.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> = 0,3251</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">In general, we
are interested in the probability of selecting <i>x </i>successes from<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">the A"
items labeled successes and <i>n — x </i>failures from the Ar — <i>k </i>items
labeled<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">failures when a
random sample of size <i>n </i>is selected from AT items. This is known<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">as a <b>hypergeometric
experiment, </b>that is, one that possesses the following two<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">properties:<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">1. A random
sample of size <i>n </i>is selected without replacement from <i>N </i>items.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">2. <i>k </i>of
the Ar items may be classified as successes and <i>N </i>— <i>k </i>are
classified as failures.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">The number X of successes
of a hypergeometric experiment is called a <b>hypergeometric<o:p></o:p></b></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">random variable.
</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Accordingly,
the probability distribution of the hypergeometric variable is called the <b>hypergeometric
distribution, </b>and its values will be denoted by <i>h(x; N, n, </i>A:),
since they depend on the number of successes <i>k </i>in the set <i>N </i>from
which we select n items.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 16.0pt;">Hypergeometric Distribution In Acceptance Sampling <o:p></o:p></span></b></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">As in the case
of the binomial distribution, the hypergeometric distribution finds applications
in acceptance sampling where lots of material or parts are sampled in order to
determine whether or not the entire lot is accepted.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Example 5.11:1 <o:p></o:p></span></b></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 21.3pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">A particular part that is used as an
injection device is sold in lots of 10. The producer feels that the lot is
deemed acceptable if no more than one defective is in the lot. Some lots are
sampled and the sampling plan involves random sampling and testing 3 of the
parts out of 10. If none of the 3 is defective, the lot is accepted. Comment on
the utility of this <b>plan.</b><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 21.3pt; text-align: justify; text-indent: -21.3pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Solution: </span></i></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Let us assume
that the lot is truly <b>unacceptable </b>(i.e., that 2 out of 10 are<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">defective). The
probability that our sampling plan finds the lot acceptable is<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">P (X = 0) = </span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>2</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>0</m:r></span></i></m:den></m:f></m:e></m:d><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>8</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>3</m:r></span></i></m:den></m:f></m:e></m:d></m:num><m:den><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>10</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>3</m:r></span></i></m:den></m:f></m:e></m:d></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -16.0pt; position: relative; top: 16.0pt;"><v:shape id="_x0000_i1025" style="height: 39pt; width: 32.25pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image006.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> =
0,467</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Thus, if the lot
is truly unacceptable with 2 defective parts, this sampling plan will allow
acceptance roughly 47% of the time. As a result, this plan should be considered
faulty. Let us now generalize in order
to find a formula for <i>h(x;N,n,k). </i>The total number of samples of size <i>n
</i>chosen from A<sup>7</sup> items is </span><!--[if gte msEquation 12]><m:oMath><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>N</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>n</m:r></span></i></m:den></m:f></m:e></m:d></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -10.0pt; position: relative; top: 10.0pt;"><v:shape id="_x0000_i1025" style="height: 26.25pt; width: 23.25pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image007.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 16.0pt;">.</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> These samples
are assumed to be equally likely. There are</span><span style="font-family: "Times New Roman","serif"; font-size: 16.0pt;"> </span><!--[if gte msEquation 12]><m:oMath><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>k</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>x</m:r></span></i></m:den></m:f></m:e></m:d></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -10.0pt; position: relative; top: 10.0pt;"><v:shape id="_x0000_i1025" style="height: 26.25pt; width: 21.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image008.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> ways of selecting <i>x </i>successes from the A*
that are available, and for each of these ways we can choose the <i>n — x </i>failures
in </span><!--[if gte msEquation 12]><m:oMath><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>N</m:r><m:r>-</m:r><m:r>k</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>n</m:r><m:r>-</m:r><m:r>x</m:r></span></i></m:den></m:f></m:e></m:d></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -10.0pt; position: relative; top: 10.0pt;"><v:shape id="_x0000_i1025" style="height: 26.25pt; width: 39pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image009.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> ways> Thus the total number of favorable
samples among the </span><!--[if gte msEquation 12]><m:oMath><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>N</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>n</m:r></span></i></m:den></m:f></m:e></m:d></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -10.0pt; position: relative; top: 10.0pt;"><v:shape id="_x0000_i1025" style="height: 26.25pt; width: 23.25pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image007.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> possible samples is given by </span><!--[if gte msEquation 12]><m:oMath><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>k</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>x</m:r></span></i></m:den></m:f></m:e></m:d><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>N</m:r><m:r>-</m:r><m:r>k</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>n</m:r><m:r>-</m:r><m:r>x</m:r></span></i></m:den></m:f></m:e></m:d></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -10.0pt; position: relative; top: 10.0pt;"><v:shape id="_x0000_i1025" style="height: 26.25pt; width: 60.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image010.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">.
Hence we have the following definition.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Hypergeometric Distribution<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">The probability
distribution of the hypergeometric random variable X, the number of successes
in a random sample of size n selected from Ar items of which <i>k </i>are
labeled <b>success </b>and <i>N — k </i>labeled <b>failure, </b>is<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<i><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">h(x; N, n, k) </span></i><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">= </span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>k</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>x</m:r></span></i></m:den></m:f></m:e></m:d><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>N</m:r><m:r>-</m:r><m:r>k</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>n</m:r><m:r>-</m:r><m:r>x</m:r></span></i></m:den></m:f></m:e></m:d></m:num><m:den><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>N</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>n</m:r></span></i></m:den></m:f></m:e></m:d></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -16.5pt; position: relative; top: 16.5pt;"><v:shape id="_x0000_i1025" style="height: 43.5pt; width: 49.5pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image011.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> , max <i>{0,
n - (N- k)}< x < min {n,k}.</i></span><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">The range of <i>x
</i>can be determined by the three binomial coefficients in the definition,<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">where <i>x </i>and
<i>n — x </i>are no more than <i>k </i>and N — A:, respectively; and both of<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">them cannot be
less than 0. Usually, when both <i>k </i>(the number of successes) and<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">N - <i>k </i>(the
number of failures) are larger than the sample size <i>n, </i>the range of a<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">hypergeometric random
variable will be <i>x </i>= 0 , 1 , . . . ,n.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Example 5.12:1 </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Lots of 40
components each are called unacceptable if they contain as many as 3 defectives
or more. The procedure for sampling the lot is to select 5 components at random
and to reject the lot if a defective is found. What is the probability that exactly
1 defective is found in the sample if there are 3 defectives in the entire lot?<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Solution: </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Using the
hypergeometric distribution with <i>n = </i>5, <i>N = 40, k — </i>3, and <i>x =
</i>1, we<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">find the probability of
obtaining one defective to be<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 134.7pt; text-align: justify;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">h</span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">(1; 40,5, 3) </span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>=
</m:r></span></i><m:f><m:fPr><span style='font-size:16.0pt;mso-ansi-font-size:
16.0pt;mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
mso-bidi-font-family:"Times New Roman";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>3</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>1</m:r></span></i></m:den></m:f></m:e></m:d><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>37</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>4</m:r></span></i></m:den></m:f></m:e></m:d></m:num><m:den><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>40</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>5</m:r></span></i></m:den></m:f></m:e></m:d></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -16.0pt; position: relative; top: 16.0pt;"><v:shape id="_x0000_i1025" style="height: 39pt; width: 57.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image012.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Once again this
plan is likely not desirable since it detects a bad lot (3 defectives)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">only about 30% of the
time.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Theorem 5.3: The mean
and variance of the hypergeometric distribution <i>h(x; N, </i>n, A;) are<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>μ</m:r><m:r>= </m:r></span></i><m:f><m:fPr><span
style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>nk</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
normal'><span style='font-size:12.0pt;line-height:115%;font-family:"Cambria Math","serif";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>N</m:r></span></i></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -9.0pt; position: relative; top: 9.0pt;"><v:shape id="_x0000_i1025" style="height: 22.5pt; width: 36pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image013.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> and </span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman";
color:red'><m:r>σ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -5.5pt; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 7.5pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image014.png">
</v:imagedata></v:shape></span><!--[endif]--><sup><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">2 </span></sup><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">= </span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman";
color:red'><m:r>N</m:r><m:r>-</m:r><m:r>n</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman";
color:red'><m:r>N</m:r><m:r>-</m:r><m:r>1</m:r></span></i></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -9.0pt; position: relative; top: 9.0pt;"><v:shape id="_x0000_i1025" style="height: 22.5pt; width: 18.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image015.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> (n)[</span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman";
color:red'><m:r>k</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
normal'><span style='font-size:12.0pt;line-height:115%;font-family:"Cambria Math","serif";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-bidi-font-family:"Times New Roman";color:red'><m:r>n</m:r></span></i></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -9.0pt; position: relative; top: 9.0pt;"><v:shape id="_x0000_i1025" style="height: 22.5pt; width: 6pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image016.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">(1-</span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman";
color:red'><m:r>k</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
normal'><span style='font-size:12.0pt;line-height:115%;font-family:"Cambria Math","serif";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-bidi-font-family:"Times New Roman";color:red'><m:r>N</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman";
color:red'><m:r>)</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -9.0pt; position: relative; top: 9.0pt;"><v:shape id="_x0000_i1025" style="height: 22.5pt; width: 11.25pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image017.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">]<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The proof for the mean
is shown in Appendix A.25.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Example 5.13:1 </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Let us now
reinvestigate Example 3.9. The purpose of this example was to illustrate<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">the notion of a random variable
and the corresponding sample space. In<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">the example, we have a lot of 100
items of which 12 are defective. What is the<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">probability that in a
sample of 10, 3 are defective?<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Solution: </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Using
the hypergeometric probability function we have<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">h</span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">(3;
100, 10, 12) = </span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>12</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>3</m:r></span></i></m:den></m:f></m:e></m:d><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>38</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>7</m:r></span></i></m:den></m:f></m:e></m:d></m:num><m:den><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>10</m:r></span></i></m:e></m:d></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -13.5pt; position: relative; top: 13.5pt;"><v:shape id="_x0000_i1025" style="height: 36.75pt; width: 43.5pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image018.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Example 5.14:1 </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Find the mean
and variance of the random variable of Example 5.12 and then use Chebyshev's
theorem to interpret the interval //. ± 2</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>σ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -5.5pt; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 7.5pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image019.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Solution: </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Since Example
5.12 was a hypergeometric experiment, with N = 40, u = 5, and<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">k = </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">3,
then by Theorem 5.3 we have<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>μ</m:r><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>(5)(3)</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>40</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>3</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>8</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>=0.375</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 29.25pt; width: 123pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image020.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>σ</m:r><m:r>2=</m:r></span></i><m:d><m:dPr><span
style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><span
style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:
12.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>40-5</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>39</m:r></span></i></m:den></m:f></m:e></m:d><m:d><m:dPr><span
style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>5</m:r></span></i></m:e></m:d><m:d><m:dPr><span
style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><span
style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:
12.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>3</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>40</m:r></span></i></m:den></m:f></m:e></m:d><m:d><m:dPr><span
style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>1-</m:r></span></i><m:f><m:fPr><span
style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:
12.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>3</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>40</m:r></span></i></m:den></m:f></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>259</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman"'><m:r>832</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>=0.3112</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 30pt; width: 255.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image021.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Taking the
square root of 0.3113, we find that <i>a </i>= 0.558. Hence the required interval
is 0.375 ± (2)(0.558), or from -0.741 to 1.491. Chebyshev's theorem states that
the number of defectives obtained when 5 components are selected at random from
a lot of 40 components of which 3 are defective has a probability of at least
3/4 of falling between - 0.741 and 1.491. That is, at, least three-fourths of the
time, the 5 components include: less than 2 defectives.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 18.0pt;">Relationship to
the Binomial Distribution<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">In this chapter
wc discuss several important discrete distributions that have wide<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">applicability.
Many of these distributions relate nicely to each other. The beginning<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">student should
gain a clear understanding of these relationships. There is an<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">interesting
relationship between the: hypergeometric and the binomial distribution.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">As one might
expect, if n is small compared to <i>N, </i>the nature of the <i>N </i>items
changes<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">very little in
each draw. So a binomial distribution can be used to approximate<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">the
hypergeometric distribution when <i>n </i>is small, compared to <i>N. </i>In
fact, as a rule<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">of thumb the
approximation is good when </span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:14.0pt;mso-ansi-font-size:14.0pt;mso-bidi-font-size:14.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>n</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>N</m:r></span></i></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -10.0pt; position: relative; top: 10.0pt;"><v:shape id="_x0000_i1025" style="height: 24.75pt; width: 7.5pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image022.png">
</v:imagedata></v:shape></span><!--[endif]--><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> < </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">0.05.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Thus the
quantity </span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:14.0pt;mso-ansi-font-size:14.0pt;mso-bidi-font-size:14.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>k</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>N</m:r></span></i></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -10.0pt; position: relative; top: 10.0pt;"><v:shape id="_x0000_i1025" style="height: 26.25pt; width: 7.5pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image023.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> plays the role of the binomial parameter <i>p.
</i>As a result, the binomial distribution may be viewed as a large population
edition of the hypergeometric: distributions. The mean and variance then come
from the formulas<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>μ</m:r><m:r>=</m:r><m:r>np</m:r><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>nk</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
normal'><span style='font-size:12.0pt;line-height:115%;font-family:"Cambria Math","serif";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>N</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r><span
style='mso-spacerun:yes'> </span></m:r><m:r><span style='color:red'>σ</span></m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -9.0pt; position: relative; top: 9.0pt;"><v:shape id="_x0000_i1025" style="height: 22.5pt; width: 87.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image024.png">
</v:imagedata></v:shape></span><!--[endif]--><sup><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">2 </span></sup><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">= npq = </span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman";
color:red'><m:r>n</m:r><m:r>.</m:r></span></i><m:f><m:fPr><span
style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman";
color:red'><m:r>k</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
normal'><span style='font-size:12.0pt;line-height:115%;font-family:"Cambria Math","serif";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-bidi-font-family:"Times New Roman";color:red'><m:r>N</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman";
color:red'><m:r>(1-</m:r></span></i><m:f><m:fPr><span style='font-size:12.0pt;
mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:"Cambria Math";
mso-bidi-font-family:"Times New Roman";color:red;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman";
color:red'><m:r>k</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
normal'><span style='font-size:12.0pt;line-height:115%;font-family:"Cambria Math","serif";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-bidi-font-family:"Times New Roman";color:red'><m:r>N</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman";
color:red'><m:r>)</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -9.0pt; position: relative; top: 9.0pt;"><v:shape id="_x0000_i1025" style="height: 22.5pt; width: 57.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image025.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Comparing those
formulas with those of Theorem 5.3, we see that the mean is the<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">same whereas the
variance differs by a correction factor of <i>(N — n)/(N </i>— 1), which<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">is negligible when <i>n
</i>is small relative to N.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 16.0pt;">Multivariate
Hypergeometric Distribution</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">If <i>N </i>items
can be partitioned into the A: cells <i>A<sub>1</sub></i>,
<i>A<sub>2</sub>,..., </i><i>A<sub>k</sub></i>
with at, <i>a.2,</i>..., <i>ak </i>elements, respectively, then the probability
distribution of the random variables X<sub>1</sub>,X<sub>2</sub>,...,X<sub>k</sub>,,
representing the number of elements selected from <i>A<sub>1</sub></i> <i>,A<sub>2</sub>,..., A<sub>k</sub> </i>in a random
sample' of size <i>n, </i>is <i><span style="color: red;">f</span></i><span style="color: red;">(x<sub>1</sub>, x<sub>2</sub>,
... x<sub>k</sub> ; a<sub>1</sub>, a<sub>2</sub>, ... a<sub>k</sub>, N, n) = </span></span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>a</m:r><m:r>1</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>x</m:r><m:r>1</m:r></span></i></m:den></m:f></m:e></m:d><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>a</m:r><m:r>2</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>x</m:r><m:r>2</m:r></span></i></m:den></m:f></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";color:red'><m:r>…</m:r></span></i><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>ak</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
normal'><span style='font-size:16.0pt;font-family:"Cambria Math","serif";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>xk</m:r></span></i></m:den></m:f></m:e></m:d></m:num><m:den><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>N</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
normal'><span style='font-size:16.0pt;font-family:"Cambria Math","serif";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>n</m:r></span></i></m:den></m:f></m:e></m:d></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -16.5pt; position: relative; top: 16.5pt;"><v:shape id="_x0000_i1025" style="height: 43.5pt; width: 77.25pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image026.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="color: red; font-family: "Times New Roman","serif"; font-size: 16.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> </span><span style="color: red; font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">with </span><!--[if gte msEquation 12]><m:oMath><m:nary><m:naryPr><m:chr
m:val="∑"/><m:limLoc m:val="undOvr"/><span style='font-size:12.0pt;
mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:"Cambria Math";
mso-bidi-font-family:"Times New Roman";color:red;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;font-family:
"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:
minor-fareast;mso-bidi-font-family:"Times New Roman";color:red'><m:r>i</m:r><m:r>=1</m:r></span></i></m:sub><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;font-family:
"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:
minor-fareast;mso-bidi-font-family:"Times New Roman";color:red'><m:r>k</m:r></span></i></m:sup><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;font-family:
"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:
minor-fareast;mso-bidi-font-family:"Times New Roman";color:red'><m:r>xi</m:r><m:r>=</m:r><m:r>n</m:r><m:r>
</m:r><m:r>dan</m:r></span></i><m:nary><m:naryPr><m:chr m:val="∑"/><m:limLoc
m:val="undOvr"/><span style='font-size:12.0pt;mso-ansi-font-size:12.0pt;
mso-bidi-font-size:12.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;
font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman";
color:red'><m:r>i</m:r><m:r>=1</m:r></span></i></m:sub><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;
font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman";
color:red'><m:r>k</m:r></span></i></m:sup><m:e><i style='mso-bidi-font-style:
normal'><span style='font-size:12.0pt;font-family:"Cambria Math","serif";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-bidi-font-family:"Times New Roman";color:red'><m:r>ai</m:r><m:r>=</m:r><m:r>N</m:r></span></i></m:e></m:nary></m:e></m:nary></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -5.5pt; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 17.25pt; width: 2in;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image027.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Example
5.16:1</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">
A group of 10 individuals is used for a biological case study. The group
contains 3 people with blood type O, 4 with blood type A, and 3 with blood type
B. What<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">is the probability that a random
sample of 5 will contain I person with blood type O, 2 people with blood type
A, and 2 people with blood type 13?<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Solution: </span></i></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Using the
extension of the hypergeometric distribution with <i>x<sub>1</sub>= </i>1, <i>x<sub>2</sub>
</i>= 2, x<sub>3</sub> = 2,<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">a<sub>I</sub> = 3, a<sub>2</sub>
= 4, a<sub>3</sub> = 3, iV = <b>10, </b>and <i>n </i>= 5, we find t h a t the
desired probability is<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">f(1,2,2;3,4,3,10,5) =</span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>3</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>1</m:r></span></i></m:den></m:f></m:e></m:d><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>4</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>2</m:r></span></i></m:den></m:f></m:e></m:d><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>3</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>2</m:r></span></i></m:den></m:f></m:e></m:d></m:num><m:den><m:d><m:dPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><m:type
m:val="noBar"/><span style='font-size:16.0pt;mso-ansi-font-size:16.0pt;
mso-bidi-font-size:16.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
"Times New Roman";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>10</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>5</m:r></span></i></m:den></m:f></m:e></m:d></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:16.0pt;mso-ansi-font-size:16.0pt;mso-bidi-font-size:16.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;font-family:
"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:
minor-fareast;mso-bidi-font-family:"Times New Roman"'><m:r>3</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:16.0pt;font-family:
"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:
minor-fareast;mso-bidi-font-family:"Times New Roman"'><m:r>14</m:r></span></i></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -16.0pt; position: relative; top: 16.0pt;"><v:shape id="_x0000_i1025" style="height: 39pt; width: 81.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\HPMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image028.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-52152171342825513812013-05-19T19:21:00.001-07:002013-05-19T19:21:03.100-07:00Sebaran Binomial dan Multinomial<br />
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Prosess Bernaulli</span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Secara langsung, proses harus mempunyai sifat-sifat berikut :</span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">1. Percobaan tersebut terdiri atas <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">n</em> coba-coba yang berulang</span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">2. Setiap coba-coba menghasilkan kaluaran yang dapat diklasifikasikan sebagai sukses atau gagal</span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">3. Probabilitas sukses, yang ditujukan oleh <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">p</em>, tetap konstan dari coba-coa satu ke coba-coba lainnya.</span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">4. Coba-coba yang berulang adalah bebas.</span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<br /></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Andaikan segulas Trial Bernoulli di mana tiga barang dipilih secara acak dari sebuah proses produsi, diperikssa, dan diklasifikasikan seagai cacat atau tidak. Suatu barang cacat ditandai dengan sukses. Jumlah sukses merupakan peubah acak X yang mengambil nilai bulat dari nol sampai 3. Delapan keluaran yang mungkin dan nilai X yang bersangkutan adalah</span></span></div>
<table border="0" frame="border" style="background-color: #f37a0b; border-collapse: collapse; border-spacing: 0px; border: 0px solid rgb(0, 0, 0); font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin: 1em 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><tbody style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">
<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Keluaran</span></span></td><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">x</span></span></td></tr>
<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="margin: 0px; outline: 0px; padding: 5px; text-align: center; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">NNN</span></span></td><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">0</span></span></td></tr>
<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="margin: 0px; outline: 0px; padding: 5px; text-align: center; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">NDN</span></span></td><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">1</span></span></td></tr>
<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="margin: 0px; outline: 0px; padding: 5px; text-align: center; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">NND</span></span></td><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">1</span></span></td></tr>
<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="margin: 0px; outline: 0px; padding: 5px; text-align: center; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">DNN</span></span></td><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">1</span></span></td></tr>
<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="margin: 0px; outline: 0px; padding: 5px; text-align: center; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">NDD</span></span></td><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">2</span></span></td></tr>
<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="margin: 0px; outline: 0px; padding: 5px; text-align: center; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">DND</span></span></td><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">2</span></span></td></tr>
<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="margin: 0px; outline: 0px; padding: 5px; text-align: center; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">DDN</span></span></td><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">2</span></span></td></tr>
<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="margin: 0px; outline: 0px; padding: 5px; text-align: center; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">DDD</span></span></td><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">3</span></span></td></tr>
</tbody></table>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Karena barang-barang tersebut dipilih secara beas dari suatu proses yang akan kita asumsikan menghasilkan 25% cacat</span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;"><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">P(NDN) = P(N) P(D) P(N) = </span><img class="latex-formula" formula="%24%5Cleft%28%20%5Cfrac%7B3%7D%7B4%7D%20%5Cright%29%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302595/latex-e9a3b768e6016e85ea9910b9baf6c23e.png" style="border: 0px; line-height: 1.4; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; word-wrap: break-word;" /> <span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> </span><img class="latex-formula" formula="%24%5Cleft%28%20%5Cfrac%7B1%7D%7B4%7D%20%5Cright%29%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302595/latex-93bad14ce1acbe891a20cf47aa86c9f3.png" style="border: 0px; line-height: 1.4; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; word-wrap: break-word;" /> <img class="latex-formula" formula="%24%5Cleft%28%20%5Cfrac%7B3%7D%7B4%7D%20%5Cright%29%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302595/latex-e9a3b768e6016e85ea9910b9baf6c23e.png" style="border: 0px; line-height: 1.4; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; word-wrap: break-word;" /><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> = </span><img class="latex-formula" formula="%24%20%5Cfrac%7B9%7D%7B64%7D%20%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302595/latex-1c2aea0dd7ba9f86d955dc353664cbdd.png" style="border: 0px; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; word-wrap: break-word;" /></span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<br /></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
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<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Perhitungan yang sama menghasilkan probabilitas bagi keluaran yang mungkin lainnya. Sebaran probabilitas X adalah </span></span></div>
<table border="0" style="background-color: #1d93e1; border-collapse: collapse; border-spacing: 0px; border: 0px solid rgb(27, 55, 227); font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin: 1em 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><tbody style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">
<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">0</sub></span></span></td><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">1</span></span></td><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">2</span></span></td><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">3</span></span></td><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">4</span></span></td></tr>
<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">f(x)</span></span></td><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span style="color: blue;"><br style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;" /><span data-mce-mark="1" style="background-color: white; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><img class="latex-formula" formula="%24%20%5Cfrac%7B27%7D%7B64%7D%20%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302595/latex-cc9b390675d13d27318e83ff0780e859.png" style="border: 0px; margin: 0px; max-width: 978px; outline: 0px; padding: 0px; word-wrap: break-word;" /></span></span></td><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span style="color: blue;"><br style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;" /><span data-mce-mark="1" style="background-color: white; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><img class="latex-formula" formula="%24%20%5Cfrac%7B27%7D%7B64%7D%20%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302595/latex-cc9b390675d13d27318e83ff0780e859.png" style="border: 0px; margin: 0px; max-width: 978px; outline: 0px; padding: 0px; word-wrap: break-word;" /></span></span></td><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span style="color: blue;"><br style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;" /><span data-mce-mark="1" style="background-color: white; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><img class="latex-formula" formula="%24%20%5Cfrac%7B9%7D%7B64%7D%20%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302595/latex-1c2aea0dd7ba9f86d955dc353664cbdd.png" style="border: 0px; margin: 0px; max-width: 978px; outline: 0px; padding: 0px; word-wrap: break-word;" /></span></span></td><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;"><span style="color: blue;"><br style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;" /><span data-mce-mark="1" style="background-color: white; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><img class="latex-formula" formula="%24%20%5Cfrac%7B1%7D%7B64%7D%20%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302595/latex-d8024f29df8fa9e3392e14410b5ee053.png" style="border: 0px; margin: 0px; max-width: 978px; outline: 0px; padding: 0px; word-wrap: break-word;" /></span></span></td></tr>
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<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
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<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Jumlah X sukses dimana n coba-coba Bernoulli disebut sebagai <span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">peubah acak binomial.<span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> Sebaran probablititas peubah acak diskrit ini disebut sebagai sebaran binomial, dan nilainya akan ditunjukkan oleh b(x;n,p), karena nilai terseut tergantung pada jumlah coba-coba dan probabilitas suatu sukses pada suatu coba-coba yang dierikan. Sehingga, untuk sebaran probabilitas X, jumlah cacat, </span></span></span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;"><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">P(X=2) = <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">f</em>(2) = b(2;3;1/4) = </span><img class="latex-formula" formula="%24%20%5Cfrac%7B9%7D%7B64%7D%20%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302595/latex-1c2aea0dd7ba9f86d955dc353664cbdd.png" style="border: 0px; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; word-wrap: break-word;" /></span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
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<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Sekarang mari kita generalisasikan gambaran di atas untuk menghasilkan suatu rumus bagi b(<em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">x;n,p</em>). Dengan kata lain, kita ingin mendapatkan suatu rumus yang memberikan probabilitas <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">x</em> sukses di dalam <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">n</em> percobaan untuk sebuah percobaan binomial.</span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Pertama, andaikan probabilitas <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">x</em> sukses dan <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">n-x</em> gagal di dalam suatu ukuran tertentu. Karena percobaan tersebut adalah bebas, maka kita dapat mengalikan semua probabilitas yang bersesuaian dengan keluaran yang berbeda. Setiap sukses terjadi dengan probabilitas <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">p</em> dan setiap gagal dengan probabilitas <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">q= 1 - p</em></span></span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;"><em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><br style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;" /></em>Sehingga, probabilitas untuk urutan tersebut adalah <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">p<sup style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">x</sup>q<sup style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">n-x. </sup></em>Sekarang kita coba menentukan jumlah total titik contoh di dalam percobaan yang menjadi <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">x</em> sukses dan <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">n-x</em> kegagalan. Jumlah ini sama dengan jumlah partisi dari <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">n</em> keluaran ke dalam dua kelompok dengan <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">x</em> di dalam satu kelompok dan <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">n-x</em> di dalam kelompok lainnya dan di tulis</span></span></div>
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<span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;"><img class="latex-formula" formula="%24%5Cleft%28%20%5Cfrac%7Bn%7D%7Bx%7D%20%5Cright%29%24" id="tme_imgModEnabled" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302595/latex-a73af2086fec490abd8d89b4b0dd062c.png" style="border: 0px; font-family: tahoma, arial, helvetica, sans-serif; font-size: medium; line-height: 22px; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; word-wrap: break-word;" /><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">. Karena partisi-partisi ini saling terpisah, kita menambahkan probabilitas semua partisi yang berbeda untuk mendapatkan rumus umum, atau mengalikan <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">p<sup style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">x</sup>q<sup style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">n-x </sup></em>dengan </span><img class="latex-formula" formula="%24%5Cleft%28%20%5Cfrac%7Bn%7D%7Bx%7D%20%5Cright%29%24" id="" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302595/latex-a73af2086fec490abd8d89b4b0dd062c.png" style="border: 0px; font-family: tahoma, arial, helvetica, sans-serif; font-size: medium; line-height: 1.4; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; word-wrap: break-word;" /></span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;"><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">Ingat <span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">!</span></span></span><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> Sebaran Binomial</span></span></span></div>
<table border="1" cellpadding="0" cellspacing="0" style="background-color: white; border-collapse: collapse; border-spacing: 0px; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin: 1em 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><tbody style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">
<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;" valign="top" width="616"><div style="line-height: 1.4; margin-bottom: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Coba-coba Bernoulli dapat menghasilkan suatu sukses dengan probabilitas p dan gagal dengan probabilitas<em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> q = 1 - p</em>. Maka, sebatan probabilitas peubah acak binomial X, jumlah sukses di dalam <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">n</em> coba-coba bebas adalah</span></span></div>
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<span style="color: blue;"><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">b(x;n,p)</em> = </span><img class="latex-formula" formula="%24%5Cleft%28%20%5Cfrac%7Bn%7D%7Bx%7D%20%5Cright%29%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302595/latex-a73af2086fec490abd8d89b4b0dd062c.png" style="border: 0px; margin: 0px; max-width: 978px; outline: 0px; padding: 0px; word-wrap: break-word;" /><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">p<sup style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">x</sup>q</em></span></span><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><sup style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">n-x</sup> , x = 0,1, 2, 3 ... n</em> </span><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> </span></span></div>
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<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
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<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Perhatikan bahwa bila n = dan p =1/4, sebaran probabilitas X, jumlah cacat, dapat ditulis sebagai</span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span style="color: blue;"><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">b(x;</em>3,1/4<em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">)</em> =</span><img class="latex-formula" formula="%24%5Cleft%28%20%5Cfrac%7B3%7D%7Bx%7D%20%5Cright%29%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302595/latex-6133413b4c52ff683f3012d015cb6284.png" style="border: 0px; line-height: 1.4; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; word-wrap: break-word;" /><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; line-height: 1.4; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> (1/4) </span><sup style="font-family: tahoma, arial, helvetica, sans-serif; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">x </sup><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; line-height: 1.4; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">(3/4) </span><sup style="font-family: tahoma, arial, helvetica, sans-serif; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">3-x</sup><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; line-height: 1.4; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">, </span><em style="font-family: tahoma, arial, helvetica, sans-serif; font-size: medium; line-height: 1.4; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> x = </em><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; line-height: 1.4; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">0,1,2,3,</span><em style="font-family: tahoma, arial, helvetica, sans-serif; font-size: medium; line-height: 1.4; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> </em></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">bukan dalam bentuk tabel di atas</span></span></div>
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<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><strong style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Contoh 2.1</span></strong></span></div>
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<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Probabilitas bahwa sejenis komponen tertentu yang akan bertahan terhadap sebuah uji-kejut adalah 3/4. Carilah probabilitas dimana 2 dan 4 komponen yang selanjutnya di uji akan bertahan.</span></span></div>
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<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><strong style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Penyelesaian </span></strong></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;"><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">Dengan mengasumsikan bahwa pengujian tersebut bebas dan <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">p</em> = 3/4 untuk masing-masing </span></span><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">dari keempat pengujian tersebut, kita dapatkan</span></span></span></div>
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<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;"><em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">b</em>(2;4,3/4)<span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> = </span><img class="latex-formula" formula="%24%5Cleft%28%20%5Cfrac%7B4%7D%7B2%7D%20%5Cright%29%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302595/latex-23db59763b04c8b518aac516ddb673c9.png" style="border: 0px; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; word-wrap: break-word;" /><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> (3/4)<sup style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sup></span><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"></span><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">(1/4)</span><sup style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span data-mce-mark="1" style="font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2 </span></sup><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">= </span><img class="latex-formula" formula="%24%5Cfrac%7B4%21%7D%7B2%212%21%7D%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302595/latex-1e1913cdf432991f5e1ee419c007753a.png" style="border: 0px; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; word-wrap: break-word;" /><em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><br style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;" /></em></span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><strong style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Teorema 1.2 </span></strong></span></div>
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<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;" valign="top" width="616"><div style="line-height: 1.4; margin-bottom: 1em; outline: 0px; padding: 0px; text-align: center; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;"> Nilai tengah dan ragam sebaran binomial <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">b(x;n;p)</em> adalah </span></span></div>
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<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">μ = np dan σ<sup style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sup> = npq</span></em></span></div>
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<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><strong style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Contoh 2.2</span></strong></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Carilah nilai tengah dan ragam dari peubah acak binomial pada contoh 2.1, kemudian gunakan teorema Chebish untuk menginterpretasikan selang μ ± 2σ.</span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><strong style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Penyelesaian</span></strong></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;"><strong style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><br style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;" /></span></span></strong><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">Karena contoh 2.1 merupakan suatu percobaan binomial dengan n = 15 dan p = 0.4; menurut Teorema 5.2, kita dapatkan</span></span></span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">μ = (15)(0.4) = 6 dan σ<sup style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sup> = (15)(0.4)(0.6) = 3.6</span></span></div>
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<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;"><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">Ingat <span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">!</span></span><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> </span> </span> <span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">Sebaran Multinomial</span></span></span></span></div>
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<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="margin: 0px; outline: 0px; padding: 5px; word-wrap: break-word;" valign="top" width="616"><div style="line-height: 1.4; margin-bottom: 1em; outline: 0px; padding: 0px; text-align: center; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;"> <span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">Jika suatu coba-coba yang diketahui dapat menghasilkan k keluaran E<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">1</sub>, E<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sub>, ..., E<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">k</sub> dengan probabilitas p<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">1</sub>, p<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sub>, ..... p<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">k</sub>, maka sebaran probabilitas peubah acak X<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">1</sub>, X<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sub>, ....., X<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">k</sub> yang mewakili jumlah kejadian untuk E<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">1</sub>, E<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sub>, ..., E<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">k</sub> di dalam n coba-coba yang bebas adalah</span></span></span></div>
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<span style="color: blue;"><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">f(x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">1</sub>,x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sub>, ... x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">k</sub>; p<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">1</sub>,p<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sub>, ... p<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">k</sub>, n) = </span><img class="latex-formula" formula="%24%5Cleft%28%5Cfrac%7Bn%7D%7BX1%2C%20X2%2C%20X3%2C%20...%2C%20Xk%7D%20%5Cright%29%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302595/latex-7130298ba7fb65f386abda06a111f267.png" style="border: 0px; margin: 0px; max-width: 978px; outline: 0px; padding: 0px; word-wrap: break-word;" /> <span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">P</span><sub style="font-family: tahoma, arial, helvetica, sans-serif; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">1</sub><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> P</span><sub style="font-family: tahoma, arial, helvetica, sans-serif; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sub><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> P</span><sub style="font-family: tahoma, arial, helvetica, sans-serif; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">k</sub></span></div>
<div style="line-height: 1.4; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; text-align: center; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">dengan</span></span></div>
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<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">∑<em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">i = n </sub></em><sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">dan</sub><em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> </sub>∑p<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">i</sub> = 1<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><br style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;" /></em></sub></em></span></span></div>
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<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Sebaran multinomial memperoleh namanya dari kenyataan bahwa suku-suku ekspansi multinomial<em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> (p<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">1</sub> + p<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sub> + ... + p<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">k</sub>)<sup style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">n</sup></em> bersesuaian dengan semua nilai yang mungkin dari<em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> f(x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">1</sub>,x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sub>, ..., x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">k</sub>; p<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">1</sub>, p<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sub>, ... p<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">k, </sub>n)<sup style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><br style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;" /></sup></em></span></span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><strong style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Contoh 2.3</span></strong></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Bila sepasang dadu dilemparkan 6 kali, berapakah proabilitas mendapatkan suatu total 7 atau 11 sebanyak dua kali, pasangan angka yang sama sekali, dan sembarang gaungan lainnya sebanyak 3 kali?</span></span></div>
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<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><strong style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Penyelesaian</span></strong></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">Kita daftar kejadian-kejadian yang mungkin berikut ini :</span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">E<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">1</sub> : Sebuah total 7 atau 11 muncul</span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">E<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sub> : pasangan angka yang sama muncul</span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span style="color: blue;">E<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">3</sub> : bukan angka sama atau bukan total 7 atau 11 yang muncul</span></span></div>
<div style="background-color: white; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 16px; margin-bottom: 1em; margin-top: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span style="color: blue;"><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">Probabilitas yang bersesuaian untuk coba-coba yang diketahui tersebut adalah p<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">1</sub> = 2/9, p<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sub> = 1/6, dan p<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">3</sub> = 11/18. Nilai-nilai ini tetap konstan untuk keenam coba-coba tersebut. Dengan menggunakan sebaran multinomial dengan x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">1</sub> = 2, x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sub> = 1 dan x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">3</sub> = 3, kita dapatkan bahwa probabilitas yang diperlukan adalah<em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> f</em>(2, 1, 3; 2/9, 1/6, 11/18, 6) =</span><span style="line-height: 1.4;"><img class="latex-formula" formula="%24%5Cleft%28%5Cfrac%7B6%7D%7B2%2C%201%2C%203%7D%20%5Cright%29%24" id="" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39302595/latex-1d9372e72c7d3e7ed00bb61ed4bb1680.png" style="border: 0px; line-height: 1.4; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; word-wrap: break-word;" /></span><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; line-height: 1.4; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> </span><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; line-height: 1.4; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> (2/9)<sup style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sup> (1/6)<sup style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sup> (11/18)<sup style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">3</sup> = 0,1127</span></span></div>
Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-32721672002935862732013-05-19T19:07:00.005-07:002013-05-19T19:12:14.625-07:00Sebaran Seragam Diskrit<table border="0" style="background-color: #23dbdb; border-collapse: collapse; border-spacing: 0px; border: 0px solid rgb(222, 32, 222); color: #333333; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 12px; line-height: 16px; margin: 1em 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><tbody style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">
<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="border-color: rgb(187, 187, 187); color: black; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; margin: 8px; outline: 0px; padding: 5px; word-wrap: break-word;"><div style="font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 12px; line-height: 1.4; margin-bottom: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="color: white; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><strong style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">Definisi</strong></span></div>
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<span style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">Sebaran Seragam Diskret. Bila peubah acak X mempunyai nilai-nilai x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">1</sub>, x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sub> .... x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">k</sub>, dengan peluang yang sama, maka sebaran seragam diskretnya di berikan oleh <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">f(x;k) = </em></span><img class="latex-formula" formula="%24%24%20%5Cfrac%7B1%7D%7Bk%7D%20%24%24" id="tme_imgModEnabled" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39300955/latex-8672b5cc629cfe6eba2be70a7e61bc09.png" style="border: 0px; color: #333333; font-family: tahoma, arial, helvetica, sans-serif; font-size: medium; margin: 0px; max-width: 978px; outline: 0px; padding: 0px; word-wrap: break-word;" /><em style="color: #333333; font-family: tahoma, arial, helvetica, sans-serif; font-size: medium; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> , x = x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">1</sub>, x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sub>, ... x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">k</sub></em></div>
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<span style="color: purple;"><span style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; line-height: 19px;">Kita telah menggunakan notasi </span><em style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; line-height: 19px; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">f(x;k) </em><span style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; line-height: 19px;">bukan</span><em style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; line-height: 19px; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> </em><em style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; line-height: 19px; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">f(x) </em><span style="background-color: white; font-family: tahoma, arial, helvetica, sans-serif; line-height: 19px;">untuk menunjukkan bahwa sebaran seragam tersebut tergantung pada parameter k.</span></span><br />
<span style="color: purple;"><br /></span><table border="0" frame="box" style="background-color: #e317e8; border-collapse: collapse; border-spacing: 0px; border: 0px solid rgb(250, 4, 250); color: #333333; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 12px; line-height: 16px; margin: 1em 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><tbody style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">
<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="border-color: rgb(187, 187, 187); color: black; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; margin: 8px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="color: purple; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">Contoh 1</span></td></tr>
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<div style="background-color: white; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px; margin-bottom: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span style="color: purple;"><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">Bila sebuah lampu dipilih secara acak dari sebuah kotak yang berisi sebuah bola lampu 40 watt, sebuah 60 watt, sebuah 75 watt, dan sebuah 100 watt. Setiap unsur ruang contoh S = {40, 60, 75, 100} terjadi dengan probabilitas </span><img class="latex-formula" formula="%24%24%20%5Cfrac%7B1%7D%7B4%7D%20%24%24" id="tme_imgModEnabled" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39300955/latex-622e54feedfd8d7620d5c393968c59da.png" style="border: 0px; font-family: tahoma, arial, helvetica, sans-serif; font-size: medium; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; word-wrap: break-word;" /><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">. Sehingga, kita mempunyai suatu sebaran seragam dengan </span><span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">f</em>(x;4) =</span></span><img class="latex-formula" formula="%24%24%20%5Cfrac%7B1%7D%7B4%7D%20%24%24" id="tme_imgModEnabled" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39300955/latex-622e54feedfd8d7620d5c393968c59da.png" style="border: 0px; font-family: tahoma, arial, helvetica, sans-serif; font-size: medium; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; word-wrap: break-word;" /><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> , x = </span><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">40</span><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">, 60, 75, 100.</span></span></div>
<table border="0" frame="box" style="background-color: #cf10ee; border-collapse: collapse; border-color: rgb(187, 187, 187); border-spacing: 0px; color: #333333; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 12px; line-height: 16px; margin: 1em 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><tbody style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">
<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="border-color: rgb(187, 187, 187); color: black; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; margin: 8px; outline: 0px; padding: 5px; word-wrap: break-word;"><span data-mce-mark="1" style="color: purple; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">Contoh 2</span></td></tr>
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<div style="background-color: white; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px; margin-bottom: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span style="color: purple;"><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">Bila sebuah dadu dilemparkan, setiap unsur ruang contoh S = {1, 2, 3, 4, 5, 6} terjadi dengan probabilitas </span><img class="latex-formula" formula="%24%24%20%5Cfrac%7B1%7D%7B6%7D%20%24%24" id="tme_imgModEnabled" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39300955/latex-8272a8448ec7060b74ed1e11273f9aff.png" style="border: 0px; font-family: tahoma, arial, helvetica, sans-serif; font-size: medium; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; word-wrap: break-word;" /><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> . Sehingga kita mempunyai sebaran seragam dengan </span><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> </span><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">f</em>(x;6)= </span><img class="latex-formula" formula="%24%24%20%5Cfrac%7B1%7D%7B6%7D%20%24%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39300955/latex-8272a8448ec7060b74ed1e11273f9aff.png" style="border: 0px; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; font-size: 12px; line-height: 1.4; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; word-wrap: break-word;" /><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> , x =1</span><span data-mce-mark="1" style="font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">, 2, 3, 4, 5, 6.</span></span></div>
<div style="background-color: white; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px; margin-bottom: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="color: purple; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">Penyajian grafik sebaran seragam dengan cara histogram selalu menghasilkan serangkaian persegi panjang dengan ketinggian yang sama. Histogram pada contoh 2 ditunjukkan dalam gambar 1.</span></div>
<div style="background-color: white; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px; margin-bottom: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="color: purple; font-family: tahoma, arial, helvetica, sans-serif; font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">Teorema 1. 1</span></div>
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<tr style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><td style="color: black; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; margin: 8px; outline: 0px; padding: 5px; word-wrap: break-word;" valign="top" width="648"><div style="font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 12px; line-height: 1.4; margin-bottom: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
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<div style="font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 12px; line-height: 1.4; margin-bottom: 1em; outline: 0px; padding: 0px; word-wrap: break-word;">
<span data-mce-mark="1" style="font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"><span data-mce-mark="1" style="color: red; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">Nilai tengah dan ragam</span> dari sebaran seragam diskret <em style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">f(x;k)</em> adalah </span></div>
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<span data-mce-mark="1" style="font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">μ=</span><img class="latex-formula" formula="%24%24%20%5Cfrac%7B1%7D%7Bk%7D%20%24%24%20%24%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39300955/latex-9c14304805336ee54e48bf6601c27b59.png" style="border: 0px; color: #333333; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; margin: 0px; max-width: 978px; outline: 0px; padding: 0px; word-wrap: break-word;" /><span data-mce-mark="1" style="font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> </span><img class="latex-formula" formula="sum_%7B%7Bi%7D%3D%7B1%7D%7D%5E%7Bk%7Dxi%24%24%20" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39300955/latex-63a085ebc02edecf78441a02207c6645.png" style="border: 0px; color: #333333; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; margin: 0px; max-width: 978px; outline: 0px; padding: 0px; word-wrap: break-word;" /> <span data-mce-mark="1" style="font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">dan σ<sup style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sup>=<span data-mce-mark="1" style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"></span></span><span data-mce-mark="1" style="font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> </span><img class="latex-formula" formula="%24%24%20%5Cfrac%7B1%7D%7Bk%7D%20%24%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39300955/latex-8672b5cc629cfe6eba2be70a7e61bc09.png" style="border: 0px; color: #333333; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; margin: 0px; max-width: 978px; outline: 0px; padding: 0px; word-wrap: break-word;" /><span data-mce-mark="1" style="font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> </span><img class="latex-formula" formula="%24%24%20%5Csum_%7B%7Bi%7D%20%3D%7B1%7D%7D%5E%7Bk%7Dxi%24%24" src="http://www.schoology.com/system/files/tutortrove_equations/m/201304/page/39300955/latex-4717d37a8936e6ba5b54e579fe79bd92.png" style="border: 0px; color: #333333; font-family: 'Lucida Grande', Tahoma, Verdana, Arial, sans-serif; margin: 0px; max-width: 978px; outline: 0px; padding: 0px; word-wrap: break-word;" /><span data-mce-mark="1" style="font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">(x<sub style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">i</sub> - μ)<sup style="margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;">2</sup></span><span data-mce-mark="1" style="font-size: small; margin: 0px; outline: 0px; padding: 0px; word-wrap: break-word;"> </span></div>
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Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-90478277677610676132013-05-12T07:30:00.001-07:002013-05-12T17:52:19.850-07:00Uwais al-QorniYa Allah, aku suka banget sama sosok Uwais al-Qorni :)<br />
<br />
Seorang ibu yang mana yang tidak mau memiliki anak seperti dia, anak yang sangat berbakti kepada ibundanya, membuat ia sangat di kenal di Langit.<br />
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Anak adalah perhiasan dunia, karena halnya ia adalah ujian. Bisa membawakan mahkota mengantarkan kedua orangtuanya ke Syurga namun juga bisa seperti bom atom yang menjeret kedua orang tuanya ke neraka. Akan seperti apakah anak kita nanti? Tergantung dengan kita sebagai orangtuanya:) Maka belajarlah dengan tekun agar bisa mendidik dan mengajarkan banyak hal untuk anak-anak kita nanti, memberinya bekal agar menjadi anak yang bagus akhlaknya. Akan seperti apa anak kita? Jawabannya ada pada diri kita sendiri:) Wallahua'alam bisshawab<br />
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Uwais al-Qorni, tidak di kenal di Bumi namun sangat terkenal di Langit. Uwais al-Qorni penghuni Langit<br />
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Baca selengkapnya yuk di sini -----> <a href="http://majelisribaathulmuhibbiin.blogspot.com/2013/05/uwais-al-qarni-terkenal-di-langit-tak.html">sosok Uwais al-Qorni</a>Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-77424168906710050972013-05-10T19:10:00.000-07:002013-05-10T19:10:19.943-07:00romantis gak yaa :)<div class="separator" style="clear: both; text-align: center;">
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<br />Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-49854565992012610622013-05-10T16:27:00.000-07:002013-05-11T00:59:05.504-07:00SahabatkuKu tulis ini untukmu wahai sahabat,<br />
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Rasanya luar biasa bisa sekali mengenalmu</div>
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Tuhan begitu baik menghendaki kita untuk saling mengenal satu sama lain, bukan hanya saling mengenal, tapi sama-sama merasa. </div>
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Sosokmu yang lembut meski terkadang suka banget ngomel-ngomel, aku benci untuk bilang ini kalau, "Aku suka ketika kamu ngomelin aku." Meski menyebalkan sungguh. Aku rasa itu tanda kamu begitu khawatirnya, begitu perhatiannya, dan begitu pedulinya padaku.</div>
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Maafin aku yang belum bisa jadi sahabat dan sekaligus saudara yang baik untuk kamu. Yang ketika kamu menangis di sudut ruang kelas kala itu dengan berita duka tentang kondisimu, aku hanya bisa cengengesan berasa sok kuat meyakinkan. Saat itu aku sangat ingin menangis di pelukanmu melihat kamu yang pucat pasi, melihat bulir-bulir air matamu. Jangan tampakkan itu padaku! Ah aku sangat suka dengan senyummu, sampai hatikah melihatmu seperti itu? Aku sangat cengeng! Kamu tau? Aku sangat cengeng. maafkan dengan senyum palsuku. Tapi aku mau kamu kuat, yang gak mudah cengeng kaya aku. Aku mau kamu jadi wanita yang tegar, gak mudah nyerah dengan kondisi buruk apapun. </div>
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<i>Allah gak akan pernah membiarkan hambaNya sangat terpuruk, kita harus percaya itu bukan?</i></blockquote>
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Berita bahagia sebelumnya yang kudengar dari lisanmu, berita bahagia yang terucap dari seorang wanita yang sangat bahagia bila mengatakan hal itu. Yah, aku tahu pasti semua wanita akan bahagia ketika mengabarkan tentang 'itu'</div>
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Aku, sangat bahagia mendengarnya sayang, sungguh!</div>
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Tidak ada alasan buatku tidak tidak bahagia merestuimu.</div>
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Tidak perlu kamu pedulikan dengan sedikit egoku yang terkadang mulai jahil</div>
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dengan emosional perasaan kehilangan, sifat yang belum begitu matang untuk sebuah kata dewasa</div>
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<i>Tapi percayalah, tidak ada satupun saudara yang akan tidak rela bila saudaranya bahagia. begitupun denganku, bahagialah kamu wahai saudaraku, bersamanya seseorang yang kamu yakini akan menjadi imam yang baik di dunia hingga mengantarkanmu ke JannahNya :)</i></blockquote>
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<i><span style="color: blue;">Bungamu ;)</span></i></div>
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Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-64435452290685979392013-05-07T20:57:00.000-07:002013-05-08T16:08:17.791-07:00Berbicara tentang kesempatan dan kesempitanNikmatnya berbagi itu kawan, luar biasa rasanya .. kamu tahu? mungkin rasanya seperti terbang melihat awan dengan sangat dekat (padahal belum pernah yang namanya naek pesawat hehe, mungkin suatu hari nanti :) mungkin).<br />
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Misalnya kita punya uang, jangan banyak- banyak dulu sampe ke pikiran bermilyar-milyar. Cukup satu juta.<br />
Satu juta di kantong. Bedakan rasa nikmatnya ketika kita menyumbangkan 10rb ke pada yg lebih membutuhkan dari 1juta itu, dengan memberi sebesar Rp500rb atau bahkan uang 1 juta kita itu, kita beri semuanya. Bedakah rasanya? Apakah kamu pernah merasakan perbedaan nikmatnya? :)<br />
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Oke, sekarang begini, misalnya kita punya uang Rp20rb, gak ada uang lagi. tok Rp20rb. Kamu pengen banget yang namanya sedekah. hayo kamu lebih akan mnyedekahkan uang 1000mu atau Rp20.000mu?<br />
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Nikmatnya memberi ketika sedang sempit itu luar biasa kawan.<br />
Pasti Allah lebih sayang kita, gk ada yang hilang dari harta yang di berikan,<br />
hanya tersimpan di segi yang berbeda, bukan hilang, hanya tersimpan.<br />
dan akan kembali bahkan berkali-kali lipat harganya. Percaya? ;)<br />
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Cukup action kita membuat Allah mencintai kita, cukuplah action kita sebagai tanda cinta kita kepadaNya.<br />
Maukah menjadi seorang hamba yang beribadah krna landasan cinta?<br />
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Oh Wahai Allahku, aku ingin mencintaiMu dengan sebenar-benarnya cinta, izinkan aku tetap belajar, belajar beribadah dengan landasan cinta. Seperti <i><b><span style="color: magenta;">seorang kekasih</span></b></i>, melakukan apapun yang di senangi kekasihnya, bukan seperti budak yang takut kepada tuannya.</blockquote>
Wahai Allahku, rasanya ingin sekali berpulang dengan membawa kemenangan dari nafsu dan kejelekanku sendiri, agar kita dapat bertemu:) Berbincang dengan cinta, penuh dengan keharmonisan. :')<br />
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UntukMU Allaku :)<br />
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<br />Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0tag:blogger.com,1999:blog-5735857266832610539.post-87818765826883628842013-04-28T17:55:00.002-07:002013-05-10T18:56:38.464-07:00Hari kemarin, 28 April 2013Puji syukur kehadirat Tuhan Yang Maha Kuasa,<br />
Terimakasih Allah, telah banyak memberikan nikmat dengan kasihNya..<br />
Banyak rasa syukur, di hari kemarin tepatnya, bisa bersilaturhmi. Rasanya luar biasa.<br />
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Kutulis di hari ini, 29 April. Ini cerita tentang hari kemaren, dimana aktivitas pagi di awali dengan berangat ke kampus untuk menghadiri BINAR Roadshow. Setibanya disana, sudah kudapati anak-anak duduk dengan kepolosannya masing-masing, terlihat juga yang masih balita bermain berlarian dengan suaranya yang khas.<br />
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Puji syukur, Kuasanya Allah yang menciptakan manusia beranak cucu.<br />
Wahai Rasulku, lihatlah, banyak sekali umatmu kini, bukankah enggau bangga melihat ini? :) Semoga sebagian besar dari umatmu adalah umat yang benar-benar mengikuti sunnahmu, mencintaimu dengan sepenuh hati, mengidolakan engkau, bukan yang lain :)<br />
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Oke, acara ini, membuat aku mempunyai kenalan baru lagi. Yah alhamdulillah, aku mengenal hambaMu yang lain Allahku. :)<br />
Semoga jalan kebaikan selalu menyertaiku, menebar jejak di hati-hati mereka dengan kebaikan, agar tersampailah pesan Rasulku untuk saling nasihat menasehati..<br />
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Usai acara, aku bersama salah seorang temanku, sebut saja dia X, pergi ke Cilegon dengan menaiki bus. Tahukah kamu? X ini sangat humoris karakternya, baik hati,dan saya lihat dia cukup simpel melihat sisi dari suatu masalah, cukup dengan leluconnya yang membuat kita yang ada di dekatnya jadi terkekek-kekek :D<br />
Ah ya, aku ingin menyampaikan satu hal, X ini sudah aku anggap sebagai saudaraku sendiri. mari menyapa X, "Hai X, sepakat kan kalau kita akan terus jadi saudara? sampe nenek dan kakek ahahhaa." Semoga limpahan rezeki selalu mengiringi untuk kamu sekeluarga ya X :)<br />
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Ceritanya kita ke Cilegon mau interview salah seorang guru yang tinggal di sana, dengan mengunjungi rumah Quri (salah seorang sahabatku yang juga sudah aku anggap sebagai saudara dekat). Bersilaturahmi ke rumahnya, berbincang-bincang dengan ibundanya yang ramah.<br />
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Ah yaa, sebelumnya, seblm nyampe cilegon, aku dan X sempat terbawa ke terminal Merak, padahal tujuan kami hanya sampai Damkar.<br />
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"sebentar lagi kita sampai." Tuturku,<br />
"masih lama."ucap X<br />
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dengan itu, yang ada selama perjalanan, satu bus rasanya hanya ada suara aku dan dia yang serius dengan obrolan, entah obrolan tentang masa kecil masing-masing sewaktu SD yang penuh dengan petualangan atau sekedar membicarakan kepolosan teman-teman kami sewaktu kecil, ah rasanya itu seperti kembali di zaman itu.<br />
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dan tibalah ada kenehan,<br />
"hey, laut."kami saling pandang,<br />
seperti berbicara lewat hati berbisik, "Kita terlalu asyik bercerita, damkar sudah jauh terlewat." hahahaha<br />
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kita turun di terminal merak, luntang lantung dengan wajah sok biasa.<br />
masuk dari satu bus ke bus lainnya, memastikan bus yang kita tumpangi benar2 melewati damkar, yang ada hanyalah, KAMI KEMBALI TURUN DARI BUS DI KARENAKAN BUS KEBANYAKAN PERGI MENUJU JAKARTA" yah :D<br />
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oke singkat cerita, sampailah bertemu dengan quri,<br />
aku di bonceng olehnya, motornya unik sekali, beberapa tempo mengeluarkan bunyi ledakan seperti peledogan(read: petasan). Mengejutkan sekali, sepanjang perjalanan, tertawa dengan senang mewarnai wajah kami :)<br />
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segini aja deh ceritanya yaaah hehe<br />
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dapet saudara baru di kediamannya quri :)<br />
kalau kata X silaturahmi itu membawa rezeki (*gara-gara si X dapet bekel buat makan malem :D )<br />
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<br />Fithri Tegarhttp://www.blogger.com/profile/16732790230928115837noreply@blogger.com0