Let a population have values x = l, 2, 3 with probabilities f(x) = 1/3 for x = l, 2, 3. (a) Find E(X) and Var(X). (b) Find the probability function for X, the average of two observations taken from...

Let a population have values x = l, 2, 3 with probabilities

f(x) = 1/3 for x = l, 2, 3.

(a) Find E(X) and Var(X).

(b) Find the probability function for X, the average of two

observations taken from this population with replacement.

(c) Find E(X) and Var(X) from the probability function in part

(b) and show that E(X) = E(X) and Var(X) = Var(X)/2.