Sebaran Seragam Kontinu

One of the simplest continuous distributions in all of statistics is the continuous

uniform distribution. This distribution is characterized by a density function

that is "flat," and thus the probability is uniform in a closed interval, say [A, B].

Although applications of the continuous uniform distribution are not as abundant

as they are for other distributions discussed in this chapter, it is appropriate for

the novice to begin this introduction to continuous distributions with the uniform

distribution.

Uniform Distribution

It should be emphasized to the reader that the density function forms a rectangle

with base B — A and constant height -g^j- As a result, the uniform distribution

is often called the rectangular distribution. The density function for a uniform

random variable on the interval [1, 3] is shown in Figure 6.1.

Probabilities are simple to calculate for the uniform distribution due to the

simple nature of the density function. However, note that the application of this

distribution is based on the assumption that the probability of falling in an interval

of fixed length within [A, B] is constant.

Example :

Suppose that a large conference room for a certain company can be reserved for no

more than 4 hours. However, the use of the conference room is such that both long

and short conferences occur quite often. In fact, it can be assumed that length X

of a conference has a uniform distribution on the interval [0, 4].

(                  (a)    What is the probability density function?

                                                                                       

(b)   What is the probability that any given conference lasts at least 3 hours?

Solution: (a) The appropriate density function for the uniformly distributed random variable

X in this situation is