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November 9th, 2009, 08:18 AM
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| |  Transformations
Hello,
A question from my homework asks if u,v,w are iid exponentially and y=u/w and z=v/w find the pdf of (y,z). I know generally how to do transformations but in this case I cant find a Jacobian since the transformation is from 3 to 2 variables. How would I go about solving this problem.
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November 9th, 2009, 01:14 PM
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Hello,
You're correct, a transformation has to be from n to n variables. (it has to be a  -diffeomorphism)
Thus just make the following transformation : (u,v,w) -> (y,z,w), then integrate with respect to w to get the "marginal" pdf of (y,z) 
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November 9th, 2009, 03:38 PM
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Thank you,
I made the necessary substitutions and found that the inverse Jacobian is W^2. I also found that (u,v,w)= (x*w,y*w,w). Where do I go from there to find f(x,y,w).
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November 10th, 2009, 01:08 PM
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Change of Variable -- the Jacobian
what's preventing you from continuing ?
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