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Math Help - Prove E[X(X-1)] = mu(mu-1)+sigma2

  1. #1
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    Question Prove E[X(X-1)] = mu(mu-1)+sigma2

    let E(X)=\mu and Var(X)=\sigma^2

    Show that E[X(X-1)] = \mu(\mu-1)+\sigma^2
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  2. #2
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    Re: Prove E[X(X-1)] = mu(mu-1)+sigma2

    Var(x)=E((X-\mu)^2)=E(X^2-2\mu X+\mu ^2)

    =E(X^2)-2\mu E(X)+\mu ^2

    =E(X^2)-2\mu ^2 + \mu ^2 = E(X^2)-\mu ^2

    So we have E(X^2)=Var(x)+\mu ^2

    You should be able to use this last line to help you in your proof. Can you take it from here?
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  3. #3
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    Re: Prove E[X(X-1)] = mu(mu-1)+sigma2

    Yes, I have it now. I was making different substitutions, but somehow missed the one you gave. :/
    Thanks!
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