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Determining Distribution using normal/chi-square

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cse63146
#1
Aug14-09, 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 chi-square with 2 degrees of freedom.

a) What is the distribution of X2 + Y2 + Z?
b) What is the distribution of W - 4/(2|X|)
c) What is the distribution of (X2 + Y2)/Z

2. Relevant equations



3. The attempt at a solution

a) X~N(0,1) Y~N(0,1) Y2~X2(1) X2~X2(1)

Let S = X2 + Y2 + Z

therefore S~X2(4)

c) X~N(0,1) Y~N(0,1) Y2~X2(1) X2~X2(1)

Let S = (X2 + Y2)/Z

therefore S~X2(1)

b) Not sure what to do about the absolute value.
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statdad
#2
Aug14-09, 11:12 AM
HW Helper
P: 1,372
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 chi-square distributions, so ...
cse63146
#3
Aug14-09, 11:35 AM
P: 452
Ah, they become an F-distribution

so S ~ F2,2

how would I handle the |X| in part b)?

Billy Bob
#4
Aug18-09, 11:33 AM
P: 392
Determining Distribution using normal/chi-square

Quote Quote by cse63146 View Post
how would I handle the |X| in part b)?
[tex]|X|=\sqrt{X^2}[/tex]
cse63146
#5
Aug18-09, 12:34 PM
P: 452
Thank you.


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