(a) Suppose that you choose three coins at random (without replacement) from a bag containing four 20p coins and five 10p coins.

(i) Find the probability mass function of the random variable counting the number of 20p coins selected.

(ii) Determine the total expected cash value of the three coins you get, giving your answer correct to the nearest penny.

(b) LetZbe a discrete random variable with()=0E(Z)=0. Does it necessarily follow that(3)=0E(Z3)=0? If yes, give a proof; if no, give a counterexample.