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Thread: A, B, C uncorrelated random variable. X=A+B, Y=B+C. Correlation of X and Y?

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    Exclamation Correlation

    Hello I'm stuck with this question. There is an identical question is this forum but it is not answered well. Can any one help please? Thanks.

    Suppose that A, B and C are uncorrelated random variables with means u1, u2, u3 and standard deviation s1, s2 and s3 respectively. If X=A+B and Y=B+C, what is the correlation of X and Y?
    Last edited by drinkingwater; Oct 15th 2012 at 06:08 AM.
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    Re: A, B, C uncorrelated random variable. X=A+B, Y=B+C. Correlation of X and Y?

    X=A+B, Y=B+C

    Corr(X,Y) = Cov(X,Y)/(√Var(X)*√Var(Y))

    Cov(X,Y) = Cov(A+B,B+C) = Var(B)+0 = (s2)

    Var(X) = Var(A+B) = s1 + s2

    Var(Y) = Var(B+C) = s2 + s3

    So : Corr(X,Y)= (s2)/[√(s1 + s2)√(s2 + s3)]
    Thanks from drinkingwater
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