F(x, y) = 1 - e^-x - e^-y + e^(-x-y), x>0, y>0. I am supposed to find P(X + Y > 3).

I am messing up somewhere along the way, and I don't know where. What I'm doing is:

1. Finding f(x, y) = F_xy(x, y), which comes to e^-x * e^-y.

2. Setting P(X + Y > 3) = 1 - P(X + Y <= 3).

3. Setting P(X + Y <= 3) = $\displaystyle \int_0^3 \int_0^{3-x} {e^{-x} e^{-y}} dy dx$

4. Solving to get 4e^-3. But the back of the book says the answer is (e^-2 - e^-3)^2.

I really have no clue what I'm doing wrong. The book is very unclear with its examples; it only gives rectangular regions.

Please help. I really need to get this done. And I am still awaiting help on this problem, which I am no closer to solving.