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  1. #1
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    Need help




    Please help me to find how to prove:

    Cov(aX+b,cY+d)=Cov(X,Y)

    Thank you in advance

    mail me rustamna@yahoo.com

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    Rust,

    Are X and Y independent? Please show some work and we'll be glad to help.

  3. #3
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    I have to prove the property of the covariance:
    Cov(aX+b,cX+d)=Cov(X,Y) for a pair of two continuous random variables (X,Y) and any constants a,b,c,d...

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    I think it should be:

    cov(aX+b, cY+d) = ac * cov(X,Y)

    and you should be able to just write out the formula for the covariance of x and y, then substitute aX+b for x and cY+d for y, then use some summation algebra.

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    yes I agree that cov(aX+b, cY+d) = ac * cov(X,Y) but it shoud be only for discreete random variables as I understand.... but (X,Y) is the continious random variables...

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    Quote Originally Posted by rust
    yes I agree that cov(aX+b, cY+d) = ac * cov(X,Y) but it shoud be only for discreete random variables as I understand.... but (X,Y) is the continious random variables...
    I don't think that discrete or continuous makes a difference....

    Anyway, I've found a link to this proof, among others:

    homepage.mac.com/j.norstad/finance/prob.pdf

    Just type in cov(ax+b,cy+d) in Google.

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