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Math Help - Variances and covariance - needs help!!!

  1. #1
    Yan
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    Variances and covariance - needs help!!!

    Express var(X+Y), var(X-Y), and cov(X+Y),X-Y) in terms of the variances and covariance of X and Y.
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  2. #2
    Flow Master
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    Quote Originally Posted by Yan View Post
    Express var(X+Y), var(X-Y), and cov(X+Y),X-Y) in terms of the variances and covariance of X and Y.
    Use the definition, for goodness sake!

    For the third:

    Cov(X + Y, X - Y) = E((X + Y)(X - Y)) - E(X + Y) E(X - Y)

    = E(X^2 - Y^2) - [{E(X) + E(Y)}{E(X) - E(Y)}]

    = E(X^2) - E(Y^2) - [E(X)]^2 + [E(Y)]^2

    and you should be able to write this in terms of Var(X) and Var(Y).
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