(adsbygoogle = window.adsbygoogle || []).push({}); 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 X^{2}+ Y^{2}+ Z?

b) What is the distribution of W - 4/(2|X|)

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.

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# Determining Distribution using normal/chi-square

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