Help with joint distributions?

[slaux89]

Homework Statement

Suppose X and Y have joint density f(x,y)=2 for 0<y<x<1. Find P(X-Y>z)

According to the textbook the answer should be (1-z)$$^{2}$$/2

Homework Equations

The Attempt at a Solution

$$\int$$ $$\int$$ 2dxdy

for x=[0, z+y] and y=[0,1]

=$$\int$$ 2(z+y) dy

=2z+1

since we are only interested in the values where y<x, we divide this by half to get

z+ 1/2

I'm clearly way off from the answer I'm suppose to get, so I would like to know where it is I went wrong. thanks!

 

[slaux89]

Nevermind, I got it now!