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Math Help - expected value

  1. #1
    Junior Member
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    expected value

    How do I prove the following:

    Let X and Y be discrete random variables. Show that
    E[(X^2)Y given X] = (X^2)E[Y given X]

    Thanks for any help.
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  2. #2
    Member
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    May 2006
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    Quote Originally Posted by BrainMan View Post
    How do I prove the following:

    Let X and Y be discrete random variables. Show that
    E[(X^2)Y given X] = (X^2)E[Y given X]

    Thanks for any help.
    E(X^2Y|X=x)=\int x^2y\ p(x,y) \ dy=x^2 \int y\ p(x,y) \ dy

    and:

     <br />
E(Y|X=x)=\int y\ p(x,y)\ dy<br />

    .
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