Show that if Q ∼ beta(1/2α, 1/2β) then βQ/α(1−Q) ∼ Fα,β.
We are given that
Thus, the pdf of Q is given by:
where B(.,.) denotes the beta funtion.
Now, let
Thus, we get:
Now, the pdf of F is given by:
which is the pdf of distribution.
Thus,
Hence Proved
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