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Statistics: F-distribution

  1. Dec 9, 2008 #1
    1. The problem statement, all variables and given/known data
    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).


    2. Relevant 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)


    3. 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!
     
  2. jcsd
  3. Dec 14, 2008 #2
    In other words, we know that if X and Y are independent, then g(X) and h(Y) are independent, but are a function of X (f1(X)) and a function of X and Y (f2(X,Y)always independent???
     
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