Beta distribution

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

<math> f(x) = \frac{x^{a-1}(1-x)^{b-1}}{\int_0^1 u^{a-1} (1-u)^{b-1}\, du} </math>

where a and b are parameters.

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

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

<math> E(X) = \frac{a}{a+b} </math>

<math> Var(X) = \frac{ab}{(a+b)^2(a+b+1)} </math>