(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given the joint density, f(x,y), derive the probability density function for Z = X + Y and V = Y - X.

2. Relevant equations

f(x,y) = 2 for 0 < x < y < 1

f(x,y) = 0 otherwise.

3. The attempt at a solution

For Z = X + Y, I can derive the fact that,

[tex]f_Z(z) = \int_{-\infty}^{\infty} f(x,z-x)dx [/tex]

The support should be 0 < x < z - x < 1? But I am kind of lost from here.

0 < x < 1 and 0 < y < 1, so 0 < z < 2? The book I am using tell me there are two cases but I have no idea how they deduced the two cases. From my very limited understanding, f(x,y) = 2 for all x,y in its support. So why are there two cases?

Thanks!

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# Homework Help: Density Function for Sums of Random Variables

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