1. Oct 29, 2015 #1

   Jonobro

   

   The Question
   Let X and Y be two independent Geometric(p) random variables. Find E[(X^2+Y^2)/XY].
   
   Formulas
   Px(k) = py(k) = pq^(k-1)
   E(x) = Σx(p(x))
   
   My attempt at a solution
   I am really struggling with this question because I want to apply the LOTUS equation but am unsure how to do it for geometric variables. Any help would be appreciated.

    

   Jonobro, Oct 29, 2015
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3. Oct 29, 2015 #2

   mfb

   

   Insights Author

   2017 Award

   Staff: Mentor

   I didn't test it but it might be easier to find E[(X^2)/(XY)] as intermediate step.

    

   mfb, Oct 29, 2015
4. Oct 29, 2015 #3

   mathman

   

   Science Advisor

   If X or Y has a non-zero probability of being 0, that expectation is infinite.

    

   mathman, Oct 29, 2015
5. Oct 29, 2015 #4

   mfb

   

   Insights Author

   2017 Award

   Staff: Mentor

   Based on the formula in post 1, the distribution starts at 1.
   
   And I checked it, the suggested intermediate step is useful.

    

   mfb, Oct 29, 2015

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