For independent random variables X and Y, we know that f(x,y) = f1(x)f2(y)where f1 is the marginal density of X and f2 is the marginal density of Y. Using this, show that:
a) E(XY) = E(X)E(Y)
b) Var(X+Y) = Var(X)+Var(Y)
You have a random sample of size n, X1,X2,...Xn. Using the result in part (b) above, find the variance of the sample mean of that sample.