Need help

rust

New Member
#3
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...
 

JohnM

TS Contributor
#4
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.
 

rust

New Member
#5
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...
 

JohnM

TS Contributor
#6
rust said:
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:

[SIZE=-1]homepage.mac.com/j.norstad/finance/prob.pdf

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