# help needed to find the correlation of the sums of uncorrelated random variables

• Oct 16th 2008, 04:35 AM
math beginner
help 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?
• Oct 16th 2008, 05:21 AM
CaptainBlack
Quote:

Originally Posted by math beginner
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?

The correlation coefficient is:

$\displaystyle \rho_{XY}=\frac{E((X-\mu_X)(Y-\mu_Y)}{\sigma_X \sigma_Y}$

CB
• Oct 16th 2008, 05:34 AM
math beginner
Do I expand the numerator like this: E((A+B-u1-u2)(B+C-u2-u3))?
• Oct 16th 2008, 05:42 AM
math 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)?
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.
• Oct 16th 2008, 07:47 AM
CaptainBlack
Quote:

Originally Posted by math 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)?