Find E[(X^2+Y^2)/XY]

  • #1
7
0
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.
 

Answers and Replies

  • #2
35,514
11,979
I didn't test it but it might be easier to find E[(X^2)/(XY)] as intermediate step.
 
  • #3
mathman
Science Advisor
7,956
498
If X or Y has a non-zero probability of being 0, that expectation is infinite.
 
  • #4
35,514
11,979
Based on the formula in post 1, the distribution starts at 1.

And I checked it, the suggested intermediate step is useful.
 

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