I am currently try to refresh my statistics knowledge and fail at the following basic question:
Given are two vectors $$x'=(x1,x2,x3,..., xk)$$ and $$y'=(y1,y2,y3,...,yk)$$ that contain sampling of two iid random variables.
The difference of the sampling average is: $$d(x,y) = m(x) - m(y)$$
m(x) and m(y) are realizations of a discrete random variable. It follows d(x,y) is also a realization of a random variable d(X,Y)
I try to determine the variance of d(X,Y) as a function of the variance var(Xi) and var(Yi)
Do I need the formula for the variance of sums: $$var(X+Y) = var(X)+var(Y) +2cov(X,Y)$$ and $$1/n * var(Y)$$ and $$ 1/n * var(X)$$ to solve the term?
Thanks! :-)