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Probability density function integral not converging

  1. Nov 19, 2011 #1
    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.
     
  2. jcsd
  3. Nov 19, 2011 #2
    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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