# Probability density function integral not converging

1. Nov 19, 2011

### ArcanaNoir

1. The problem statement, all variables and given/known data
Let $f(x,y)=xe^{-xy}$ $x \geq 0, y \geq 1$
is this a probability density function? If not, find a constant that makes it a pdf.

2. Relevant equations

To be a pdf, we must have $\int_1^\infty \int_0^\infty \! xe^{-xy} \, \mathrm{d} x \mathrm{d} y=1$

3. The attempt at a solution

My problem is, I find the integral to be not convergent. So does my calculator. Do I have the bounds wrong? What's wrong here?

And don't mind the infinity in the integral, I know you're supposed to put the limit as some dummy variable goes to infinity.

2. Nov 19, 2011

### ArcanaNoir

Never mind, I reversed the order of integration and everything was fine. It didnt occur to me you could do that, new material.