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Beta distribution

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

where a and b are parameters.

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: