I solved majority of the question I just need to find the last joint density. Found the equations at part 3.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Show P(X-Y=z ,Y=y) = P(X) = P(|Y|)

I showed P(X) = P(|Y|)

2. Relevant equations

3. The attempt at a solution

P(X=x,Y=y) = [itex]\frac{2*(2x-y)}{\sqrt{2πT^3σ^6}}[/itex] * exp((([itex]\frac{-(2x-y)^2}{(2σ^2T)}[/itex]))

P(Y=y) = NormalPDF(0,Tσ^2)

P(X=x) = 2*NormalPDF(0,Tσ^2)

I don't really want to find the convolution then the Jacobian unless I have to. If there is an easier way please let me know.

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# Homework Help: Joint convolution?

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