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Determining Distribution using normal/chisquare 
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#1
Aug1409, 10:09 AM

P: 452

1. The problem statement, all variables and given/known data
Suppose X,W,Y and Z are all independent. X & Y have a normal distribution. W has N(4,4) distribution while Z has a chisquare with 2 degrees of freedom. a) What is the distribution of X^{2} + Y^{2} + Z? b) What is the distribution of W  4/(2X) c) What is the distribution of (X^{2} + Y^{2})/Z 2. Relevant equations 3. The attempt at a solution a) X~N(0,1) Y~N(0,1) Y^{2}~X^{2}_{(1)} X^{2}~X^{2}_{(1)} Let S = X^{2} + Y^{2} + Z therefore S~X^{2}_{(4)} c) X~N(0,1) Y~N(0,1) Y^{2}~X^{2}_{(1)} X^{2}~X^{2}_{(1)} Let S = (X^{2} + Y^{2})/Z therefore S~X^{2}_{(1)} b) Not sure what to do about the absolute value. 


#2
Aug1409, 11:12 AM

HW Helper
P: 1,371

Your response to c isn't correct  you cannot say that because the numerator has 2 degrees of freedom, as does the denominator, they cancel.
You do know that the numerator and denominator are independent, and both have chisquare distributions, so ... 


#3
Aug1409, 11:35 AM

P: 452

Ah, they become an Fdistribution
so S ~ F_{2,2} how would I handle the X in part b)? 


#4
Aug1809, 11:33 AM

P: 392

Determining Distribution using normal/chisquare



#5
Aug1809, 12:34 PM

P: 452

Thank you.



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