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If X and Y has joint pdf, f(x,y) =1 0 < x < 1, 0 < y < 1, and we want to find the pdf of Z = X +Y what is an easy way to do this? The hard part about this problem is determining the limits. When I employ the Jacobian method, I create another variable Q = Y and find the pdf of Z and Q. But when I find the marginal of Z, the bounds for Q is between 0 and z where 0 < z < 1 since Q = Y. But what happens if 1 < z < 2? I am stuck in finding the pdf.

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    You tried and failed in using the Jacobian method. I suggested to you a simpler method, **which I had also suggested to you in response to a [question of yours](http://math.stackexchange.com/q/74085/15941) about five months ago in an answer that you accepted**. Yes, the Jacobian method will work here. **You** can use the Jacobian method if you like; **I** will refuse to use the Jacobian method in solving this problem, and I will not help you with doing it that way either. Wait for someone else to post the complete answer via the Jacobian method.2012-02-29

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The condition is $0\leqslant Q\leqslant Z$ if $0\leqslant Z\leqslant1$ and $Z-1\leqslant Q\leqslant 1$ if $1\leqslant Z\leqslant2$.