Originally Posted by

**gablar** hello. I'm working on this problem. I hope someone can help me. I have worked a solution but I'm not confident about it.

**Problem:**

Express var(X+Y), var(X-Y) and cov(X+Y,X-Y) in terms of the variances and covariance of X and Y

**My attempt**:

Looking through references I found this identity:

var(X+Y)=var(X) + var(Y) + 2cov(X,Y)

This seems clear enough, although I don't know how to arrive at that solution, so it really doesn't solve my problem. I think that var(X-Y) and cov(X+Y,X-Y) can be derived from the above formula using substitutions. Can anyone point me in the right direction? I'm not sure I am understanding the question.