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Math Help - help needed to find the correlation of the sums of uncorrelated random variables

  1. #1
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    help needed to find the correlation of the sums of uncorrelated random variables

    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?
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  2. #2
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    Quote Originally Posted by math beginner View Post
    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?
    The correlation coefficient is:

    \rho_{XY}=\frac{E((X-\mu_X)(Y-\mu_Y)}{\sigma_X \sigma_Y}

    CB
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  3. #3
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    Do I expand the numerator like this: E((A+B-u1-u2)(B+C-u2-u3))?
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  4. #4
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    Is E(XY) in this case equal to E((A+B)(B+C)) = E(AB + AC+BB + BC) = E(AB) + E(AC) + E(BB) + E(BC)?
    I am not sure about this step.
    If this step is correct, I can find correlation by finding E(XY) minus the product of mean of X and mean of Y and divide that by the product of the standard deviation of X and the standard deviation of y

    I would greatly appreciate your help.
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by math beginner View Post
    Is E(XY) in this case equal to E((A+B)(B+C)) = E(AB + AC+BB + BC) = E(AB) + E(AC) + E(BB) + E(BC)?
    I am not sure about this step.
    Yes

    If this step is correct, I can find correlation by finding E(XY) minus the product of mean of X and mean of Y and divide that by the product of the standard deviation of X and the standard deviation of y
    If you have the brackets in the right place in that statement yes.

    CB
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  6. #6
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    Actually, I'm convinced that I have made a mistake in expanding E(XY) by multiplying X and Y. I'm really confused with this problem Is it possible to seek help?
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