UNIFORM DISTRIBUTION (CONTINUOUS VARIABLE) - Quantitative Techniques for management

A continuous random variable X is said to be uniformly distributed in a close interval(a, b) with probability density function p(X)if P(X ) = 1/Β-Α for Α≤X≤Β and = 0 Otherwise The Uniform distribution is alternatively known as rectangular distribution.The diagram of the probability density function is shown in the figure.

probability density function

probability density function

Example : The buses on a certain route run after every 20 minutes. If a person arrives at the bus stop at random, what is the probability that

(a) he has to wait between 5 to 15 minutes,

(b) he gets a bus within 10 minutes,

(c) he has to wait at least 15 minutes.

Solution: Let the random variable X denote the waiting time, which follows a uniform


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