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

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  1. Oct 29, 2015 #1

    Jonobro

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    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
  2. jcsd
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  3. Oct 29, 2015 #2

    mfb

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    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

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    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

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    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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