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Math Help - Suppose E[Y|X]=1. Show Cov(Y,X)=0.?

  1. #1
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    Suppose E[Y|X]=1. Show Cov(Y,X)=0.?

    Suppose E[Y|X]=1. Show Cov(Y,X)=0.?

    Please help!!

    EDIT: GOT IT, nevermind
    Last edited by Azalea; September 17th 2011 at 06:37 PM.
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  2. #2
    MHF Contributor
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    Re: Suppose E[Y|X]=1. Show Cov(Y,X)=0.?

    just for fun, since the OP has the answer anyway:

    first:
    E(Y) = E_xE(Y|X) = E_x(1) = 1

    and
    E(XY)=E_x(E(XY|X)) = E_x(E(X|X)E(Y|X)) = E_x(X \cdot 1)
    = \sum x P(X=x)
    = E(X)

    Then
    Cov(X,Y) = E(XY) -  E(Y)E(X)  = E(X) - 1 \cdot E(X) = 0
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