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Math Help - standard deviation of 0.7X + 0.3Y?

  1. #1
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    standard deviation of 0.7X + 0.3Y?

    X is normal with mean 9 and standard deviation 19
    Y is normal with mean 11 and standard deviation 17
    edit: the correlation between them is 0.6

    What is the standard deviation of 0.7X + 0.3Y? I think I may know, but I want to be sure I'm getting it right.
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  2. #2
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    ok , i'M not sure

    here is my answer

    0.7(19)+0.3(17) , i know it's simple
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  3. #3
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    I don't think that is correct, based on rules for the standard deviation.

    Could someone else help me with it please?
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  4. #4
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    Quote Originally Posted by paulrb View Post
    X is normal with mean 9 and standard deviation 19
    Y is normal with mean 11 and standard deviation 17
    edit: the correlation between them is 0.6

    What is the standard deviation of 0.7X + 0.3Y? I think I may know, but I want to be sure I'm getting it right.
     <br /> <br />
Var(aX+bY)=a^2Var(X)+b^2Var(Y)+2abCov(X,Y)<br />

    Standard Deviation= \sqrt{variance}
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  5. #5
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    Thanks, I thought that's the formula I should use, but I wasn't sure of the relation between correlation and covariance?

    is cov(X,Y) = (std. deviation X)(std. deviation X)(correlation) ?
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  6. #6
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    correlation=COV(X,Y)/(STD Dev-x *STD Dev y)

    I'm sorry, I misread correlation for covariance
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