Joint Density Probability Question

[shespuzzling]

Homework Statement

I am having trouble understanding the results of a homework problem and want to make sure I'm doing it right. The problem states that the joint density f(x,y) is equal to 1 in the shaded area and 0 elsewhere. The graph for f(x,y) looks like the attachment. The problem asks you to find F(z) and f(z) where Z=X+Y.

Homework Equations

I started to solve this by computing the double integrals (sorry, don't know how to use math fonts here).

Integral as y goes from 0 to 1, and x goes from 0 to (z-y) of f(x,y)
Integral as y goes from -1 to 0, and x goes from (z-y) to 0 of f(x,y)

I got as the solutions z-(1/2) and -z-(1/2), respectively. So adding them together you'd get F(z) to equal -1, which doesn't make any sense.

Any help/guidance would be apprecaited.

 

[lippyka]

Thanks! The attempt at a solutionI started to solve this by computing the double integrals (sorry, don't know how to use math fonts here).Integral as y goes from 0 to 1, and x goes from 0 to (z-y) of f(x,y) Integral as y goes from -1 to 0, and x goes from (z-y) to 0 of f(x,y)I got as the solutions z-(1/2) and -z-(1/2), respectively. So adding them together you'd get F(z) to equal -1, which doesn't make any sense. Any help/guidance would be apprecaited. Thanks!