Continuous random variable

Uniform distribution

A uniformly distributed random variable represents the selection of a real number completely randomly over a given interval . It is the simplest continuous distribution.

It has the following probability density function and Cumulative distribution function

Properties

Let .

1. Expectation:
2. Variance:
3. Moment-generating function:

Standard form

The standard uniform distribution is particularly useful, as it is a natural starting point for transforming random variables. See Universality of the uniform distribution

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