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Show if X ~ F( p, q) , then [(p/q) X]/[1+(p/q)X] ~ beta (p/2, q/2). Use...

Show if X ~ F( p, q) , then [(p/q) X]/[1+(p/q)X] ~ beta (p/2, q/2). Use transformation method.

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Answer #1

ssecond method:-

X~ F(p,q)

For F-distribution

where

Then

and W and V are independent

Here

Then

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