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## Homework Statement

Z = X - Y and I'm trying to find the PDF of Z.

## Homework Equations

Convolution

## The Attempt at a Solution

Started by finding the CDF:

Fz(z) = P(Z ≤ z)

P(X - Y ≤ z)

So I drew a picture

So then should Fz(z) be:

since, from my graph, it looks as though Y can go from negative infinity to positive infinity, and X can go from negative infinity on the left but is bounded by z+y on the right

then should the pdf be:

Edit: sorry I forgot to include the fact that, because fx and fy are independent, f(x,y) = fxfy in the following derivation

?

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