3. (6 points) Let X1, ..., Xn be a random sample from a distribution with mean u and variance of. Here, X is the sample mean of X1, ..., Xn. (a) Show that E(X, - X)2 = (EX?) -nx2. (b) Show that E(EX?) = n(u2 + 02) [Hint: E(Y2) = Var(Y) + [E(Y)]2. ] (c) Show that E(nx2) = nu2 + 02. [Hint: Apply the similar relation given in the previous hint]