# Need help with setting up 2 double integrals

1. Mar 29, 2009

### cse63146

1. The problem statement, all variables and given/known data

I'm trying to find the CDF of e^-y.

The cdf of any f(x,y) is $$\int^x_{-\infty} \int^y_{-\infty} f(u,v) dv du$$

where u and v are just dummy variables. I need to consider 2 cases: 1) 0<x<y and 2) 0 < y < x. In other words I need to do 2 double integrals using the general set up of a CDF.

2. Relevant equations

3. The attempt at a solution

$$\int^x_0\int^y_x e^{-v} dv du$$ This case is when 0<x<y

$$\int^x_0\int^x_y e^{-v} dv du$$ This case is when 0<y<x

Did I set these up correctly? Because a friend of mine had 2 different answers, and I made a mistake somewhere. Thank you.