(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let [itex] f(x,y)=xe^{-xy} [/itex] [itex] x \geq 0, y \geq 1 [/itex]

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 [itex] \int_1^\infty \int_0^\infty \! xe^{-xy} \, \mathrm{d} x \mathrm{d} y=1 [/itex]

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.

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# Probability density function integral not converging

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