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Joint convolution?

  1. Dec 4, 2011 #1
    I solved majority of the question I just need to find the last joint density. Found the equations at part 3.

    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.
     
    Last edited: Dec 4, 2011
  2. jcsd
  3. Dec 4, 2011 #2
    I took a step ahead and said:

    P(X=x, Y=y) = P(X-Y=x-y , Y=y) = P(Z=z, Y=y) but I don't seem to get the right distribution.
     
  4. Dec 4, 2011 #3
    Ignore the question There was a typo at the question. I just solved it Thanks
     
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