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?

- October 16th 2008, 05:35 AMmath beginnerhelp 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?

- October 16th 2008, 06:21 AMCaptainBlack
- October 16th 2008, 06:34 AMmath beginner
Do I expand the numerator like this: E((A+B-u1-u2)(B+C-u2-u3))?

- October 16th 2008, 06:42 AMmath beginner
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. - October 16th 2008, 08:47 AMCaptainBlack
Yes

Quote:

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

CB - October 16th 2008, 02:52 PMmath beginner
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 (Headbang) Is it possible to seek help?