Beta distribution:
B(a,b) = (G(a+b)/G(a)G(b))*pow(r,a-1)*pow(r,b-1)
(G(a)*G(b)/G(a+b)) = integ(pow(r,a-1)*pow(r,b-1)*dr) //range 0 to 1 over r
Gamma function:
G(a) = fact(a-1)
a*G(a) = G(a+1)
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