In probability theory and statistics, the Beta distribution is a family of continuous probability distributions defined on the interval [0,1] parametrized by two non-negative shape parameters, typically denoted by alpha and beta.

f(x,alpha,beta) =   (x^(alpha-1)*(1-x)^(beta-1))/Beta(alpha,beta)

where Beta (the beta function) is a normalization constant to ensure that the total probability is 1 and has next formula

Beta(alpha,beta) = integral from 0 to 1 of t^(alpha-1)*(1-t)^(beta-1) dt.