(a) There are 1000 households in a town. Specifically, there are are 100 households with one member, 200 households with 2 members, 300 households with 3 members, 200 households with 4 members, 100 households with 5 members, and 100 households with 6 members. (i) We pick a household at random, and define the random variable X as the number of people in the chosen household. Find the PMF and the expected value of X. (ii) We pick a person in the town at random, and define the random variable Y as the number of people in the household where the chosen person lives. Find the PMF and the expected value of Y. (b) Let X be the number facing upwards after the single roll of a fair die. (i) What is the moment generating function Mx(t)? (ii) Suppose that ten such dice are rolled independently and Y is the sum of the numbers on all the dice. What is the moment generating function My(t)