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Math Help - Question on Covariance

  1. #1
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    Question on Covariance

    I'm stuck with this problem.

    U= X, V= X^2

    What is the Cov(X,V)?

    It's supposed to come down to a clean answer.

    Thanks in advance
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  2. #2
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    Re: Question on Covariance

    Hey rokman54.

    From the definition we know Cov(X,Y) = E[XY] - E[X]E[Y] and if Y = X^2 then we get

    Cov(X,Y)
    = E[X*X^2] - E[X]E[X^2]
    = E[X^3] - E[X]E[X^2].

    Now if you want you can relate the variance to the above quantity by noting Var[X] = E[X^2] - E[X]^2 where E[X^2] = Var[X] + E[X]^2 where

    = E[X^3] - E[X](Var[X] + E[X]^2]
    = E[X^3] - E[X]Var[X] - E[X]^3
    = E[X^3] - E[X]^3 - E[X]Var[X]

    Now Consider E[X^3] and E[X]^3 and the relation to other moments if you want other simplifications.

    Did you intend to get the solution in terms of a particular moment of X (like variance, kurtosis, etc)?
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