Let X1 and X2 have independent gamma distributions with parameters α, θ and β, θ, respectively. Let W = X1/(X1 + X2). Use a method similar to that given in the derivation of the F distribution (Example 5.2-4) to show that the pdf of W is

We say that W has a beta distribution with parameters α and β.

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Г(а + B) 0 < w < 1. wa-1(1-w)B-1, 8(w) = Г(а)Г(8)