Probability density function integral not converging

  • Thread starter ArcanaNoir
  • Start date
  • #1
768
4

Homework Statement


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.


Homework 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]

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.
 

Answers and Replies

  • #2
768
4
Never mind, I reversed the order of integration and everything was fine. It didnt occur to me you could do that, new material.
 

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