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Expected value of (X/Y)

  1. Mar 11, 2014 #1
    1. The problem statement, all variables and given/known data
    Let x and y be discrete random variables with joint probability density function

    P(X,Y)= 2X-Y+1/9 for x=1,2 and y=1,2
    0 Otherwise

    Calculate E[X/Y]


    2. Relevant equations

    E[XY]= ∫∫XYP(X,Y)dxdy



    3. The attempt at a solution

    I can't find a property of Expected value to make E[X/Y] solvable. This is my best guess.
    E[X/Y]= ∫∫X*1/YP(X,1/Y)dxdy

    E[X/Y]=∫∫X*1/Y*(2X-1/Y+1/9)dxdy from 1 to 2 on the first integral and 1 to 2 on the second integral
     
  2. jcsd
  3. Mar 11, 2014 #2

    Simon Bridge

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    looks like you have a discrete probability function there.
    there are only 4 states, so why not work out X/Y for each state and find the expectation by weighted sum?
     
  4. Mar 11, 2014 #3
    I'm just not sure how to calculate E(X/Y). Is what I wrote right?
     
  5. Mar 11, 2014 #4

    Simon Bridge

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    You can answer that one yourself!

    Consider: what you wrote involves some integrals.
    Are integrals associated with continuous or discrete probability functions?
    What kind do you have?
     
  6. Mar 12, 2014 #5

    Ray Vickson

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    What you wrote is wrong. You seem to be suffering from the disease of writing formulas without knowing what they mean or when they should be used, and the prognosis of that disease is not good. Integrals are used with continuous random variables having probability density functions. Do you see any such random variables in your problem?
     
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