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Math Help - Covariance/variance with two random variables

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    Covariance/variance with two random variables

    So, the question/problem I have is this: Prove that the Cov(x,x) = Var(x)

    I had the idea to use the definition of cov(x,y) = sum all x sum all y of (x-E(x))(y-E(y))p(x,y), and by plugging in x for y i would then have two sums over all x of (x-E(x))^2 * p(x,x)
    the definition of var(x) is the sum over all x of (x-E(x))^2 * p(x)

    is it okay to say that p(x,x) = p(x)?
    Also, how do i get rid of that second summation?
    Thanks!!
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    Hello,
    Quote Originally Posted by mistykz View Post
    So, the question/problem I have is this: Prove that the Cov(x,x) = Var(x)

    I had the idea to use the definition of cov(x,y) = sum all x sum all y of (x-E(x))(y-E(y))p(x,y), and by plugging in x for y i would then have two sums over all x of (x-E(x))^2 * p(x,x)
    the definition of var(x) is the sum over all x of (x-E(x))^2 * p(x)

    is it okay to say that p(x,x) = p(x)?
    Also, how do i get rid of that second summation?
    Thanks!!
    Use the fact that cov(X,Y)=E[(X-E(X)) (Y-E(Y))] (it's equivalent to what you said...)

    So cov(X,X)=E[(X-E(X))^2]

    but this is the definition of the variance... ?
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  3. #3
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    Yeah, I saw that when I took another look at it earlier today. Thank you!
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