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:
where Γ and B are respectively the gamma function
and the beta function
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: