Beta Distribution:

Suppose x₁, x₂, ... , x_n are n independent values of a random variable uniformly distributed within the interval [0,1]. If you sort the values in ascending order, then the k-th value will have a beta distribution with parameters a = k, b = n-k+1. The density of beta distribution is given by

where a > 0, b > 0; G(·) is the gamma function.

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