Please help me to find how to prove:

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

Thank you in advance

mail me rustamna@*****.com

Rust,

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

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...

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.

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...

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 (http://www.homepage.mac.com/j.norstad/finance/prob.pdf)

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