Covariance of two sample means
I am looking to calculate VAR(xbar-ybar) where X and Y are not independent.
Want to try VAR(xbar) +VAR(ybar)+2COV(xbar,ybar).
I know VAR(xbar) = sigma^2 of X / n1
I know VAR(ybar) = sigma^2 of Y / n2
But the COV(xbar,ybar) has me stumped. I wanted to write
(1/n1)* (1/n2) * COV (SUM(Xi) 1 to n1, SUM(Yi) 1 to n2).
I have researched the additive rule of COV(X+Y,Z) = COV(X,Y) + COV(Y,Z) but not sure how to apply with a sum in both 'places' for COV(X,Y).