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kingwinner
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Homework Statement
Suppose the random variable X has a N(5,25) dsitribution and Y has a N(2,16) distribution and that X and Y are independent. Find a random variable F that is a function of both X and Y such that F has a F-distribution with parameters (1,2), i.e. F(1,2).
Homework Equations
Definition: If X~chi square(n), Y~chi square(m), and X and Y are independent, then (X/n)/(Y/m)~F(n,m)
The Attempt at a Solution
Does F=[(X-5)/5]^2 / {([(X-5)/5]^2 + [(Y-2)/4]^2])/2} work?
The only trouble I am seeing is that (X-5)/5]^2 and [(X-5)/5]^2 + (Y-2)/4]^2] might not be independent. So are they independent? If so, how can I prove it? If not, what else can I do?
Any stat guy here?
I appreciate for any help!