# covariance problem

• Dec 13th 2009, 10:53 AM
ixi
covariance problem
Let X1, X2, and X3 be uncorrelated random variables, each with mean u and variance sigma^2. Find, in means of u and sigma^2, Cov(X1+X2, X2+X3)

I got this far:

Cov(X1+X2, X2+X3) = E[(X1+X2)(X2+X3)] - E(X1+X2)E(X2+X3)

But i don't know how to continue this problem

thanks
• Dec 13th 2009, 11:42 AM
Laurent
Quote:

Originally Posted by ixi
Let X1, X2, and X3 be uncorrelated random variables, each with mean u and variance sigma^2. Find, in means of u and sigma^2, Cov(X1+X2, X2+X3)

I got this far:

Cov(X1+X2, X2+X3) = E[(X1+X2)(X2+X3)] - E(X1+X2)E(X2+X3)

But i don't know how to continue this problem

thanks

Now expand, use linearity of the expectation, and the assumptions...
• Dec 13th 2009, 06:25 PM
matheagle
I just obtain the 4 covariances...

$\displaystyle Cov(X_1+X_2, X_2+X_3)= Cov(X_1,X_2)+Cov(X_1,X_3)+Cov(X_2,X_2)+Cov(X_2,X_3 )$

$\displaystyle = 0+0+V(X_2)+0=\sigma^2$

It's just like $\displaystyle (a+b)(c+d)=ac+ad+bc+bd$