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

Given

f(x,y) = x + y 0≤x≤1, 0≤y≤1

zero , otherwise

Show that X+Y has density f(z) = z^2, 0 < z < 1, and z(2-z), 1 < z < 2.

2. Relevant equations

Also, how to find the density f(z) for X*Y?

3. The attempt at a solution

Even if f(z) is not given, some questions asks to find f(z) like what I wrote in the relevant question. My problem is how to find the limits of the integration, and how I know that I would have 0 < z < 1, and 1 < z < 2. I'm struggling with this problem since last week, and I really need your help.

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# One Function of Two Random Variables

Can you offer guidance or do you also need help?

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