Independent random variables X and Y have probability distributions as shown in the tables: 0 1 2 3 P(X-x) 0.3 0.2 0.4 0.1 0 1 0.4 0.2 0.4 y P(Y-y)

(a) Find E(X), E(Y), Var(X), Var(Y).

(b) Construct the probability distribution for the random variable X+ Y.

(c) Verify that E(X + Y) E(X) + E(Y).

(d) Verify that Var(X + Y) Var(X) + Var(Y).

(e) Construct the probability distribution for the random variable X-Y.,

(f) Verify that E(X-Y) E(X) E(Y). (g) Verify that Var(X-Y)-Var(X) + Var(Y).