I am having difficulty understanding a homework problem. I've attached what was given as the joint density of x & y (1 in the shaded area, 0 everywhere else).
We're asked to find F(z) and f(z) where Z=X+Y
I attempted to solve this by computing two double integrals, one for 0<z<1 and one for -1<z<0. For the first, I made y go from 0 to 1 and x go from 0 to z-y, and for the second, y went from -1 to 0, and x went from z-y to 0. The answer for each integral, respectively, was z-(1/2) and -z-(1/2).
I can't figure out how this would make sense, because adding the two gives you a negative number. Any help/guidance would be greatly appreciated.