A continuous r.v. is said to have the Beta Distribution with parameters and , where , if its PDF is
where the constant is chosen to make the PDF integrate to . We write this as
By definition, the constant satisfies
which is the beta function
A continuous r.v. X is said to have the Beta Distribution with parameters a and b, where a,b>0, if its PDF is
f(x)=β(a,b)1xa−1(1−x)b−1,0<x<1where the constant β(a,b) is chosen to make the PDF integrate to 1. We write this as X∼Beta(a,b)
By definition, the constant β(a,b) satisfies
β(a,b)=∫01xa−1(1−x)b−1dxwhich is the beta function