====== Beta Distribution ======

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.//


^Parameter^Description               ^Default value^Restriction^
|alpha        |The first shape parameter |2.0          |alpha>0        |
|beta         |The second shape parameter|2.0          |beta>0         |