In probability theory and statistics, the **beta distribution** is a continuous probability distribution with the probability density function defined on the interval [0, 1]:

When the "constant" is included explicitly, the density looks like this:

The special case of the beta distribution, when *a* = 1 and *b* = 1, is the standard uniform distribution.

The expected value and variance of a beta random variable *X* with parameters *a* and *b* are given by the formulae: