- #1
yamdizzle
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I solved majority of the question I just need to find the last joint density. Found the equations at part 3.
Show P(X-Y=z ,Y=y) = P(X) = P(|Y|)
I showed P(X) = P(|Y|)
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.
Homework Statement
Show P(X-Y=z ,Y=y) = P(X) = P(|Y|)
I showed P(X) = P(|Y|)
Homework Equations
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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