One Function of Two Random Variables

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Homework Statement



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.


Homework Equations


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.
 

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