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Homework Statement
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
Homework Equations
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.