Thread: 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

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...

I just obtain the 4 covariances...





It's just like