Suppose X and Y have the same distribution and Corr(X,Y) = -0.5. What is V[X + Y] ?
I know that V[X + Y] = V[X] + V[Y] + 2Cov(X,Y)
and Corr(X,Y)*SD[X]SD[Y] = Cov(X,Y)
But there's clearly a missing link, maybe some identity that I'm not getting. I'm pretty sure the fact that they're the same distribution comes into play but I'm not sure how.
Thanks!
I know that V[X + Y] = V[X] + V[Y] + 2Cov(X,Y)
and Corr(X,Y)*SD[X]SD[Y] = Cov(X,Y)
But there's clearly a missing link, maybe some identity that I'm not getting. I'm pretty sure the fact that they're the same distribution comes into play but I'm not sure how.
Thanks!