"Prove that, for any real number c and any discrete random variable X, Var[cX] = c2Var(X).

Which of the following arguments proves the claim?

(a)Var(cX) = E(cXE(cX))2= E(cX)2E(cX)2 = c2E(X2)cE(X)2 = c2E(X2) c2(EX)2 = c2Var(X)

(b)Variance is an expectation= Var(cX) = c2Var(X).

(c)Use Var(cX) = E(cX2) (E(cX))2 = cE(X2) {c E(X)}2= c2Var(X).

(d)Var(cX) = Var(c)Var(X) = c2Var(X).

(e)none of these"