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