4. (3 points) Let X1,,Xn be a random and independent sample from a distribution with mean and variance 2. Here, X is the sample mean of X1,,Xn. (a) (1 points) Show that (XiX)2=(Xi2)nX2. (b) (1 points) Show that E(Xi2)=n(2+2)[Hint:E(Y2)=Var(Y)+[E(Y)]2.] (c) (1 points) Show that E(nX2)=n2+ 2. [Hint: Apply the similar relation given in the previous hint.