Probability and Statistics for Engineers and Scientists, Updated 9th Edition, by Pearson

Chapter 6

Some Continuous Probability Distributions

6.1 Continuous Uniform Distribution

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 those 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

The density function of the continuous uniform random variable X on the interval [A, B] is

The density function forms a rectangle ...