(4) Solve the following problems. (a) [3pts] There are twenty people nominated for an award, and Alfa, Bravo, and Charlie are in the nominees. There are ten judges, and each judge votes for exactly one nominee. The decision of each judge is independent. Let X be the number of votes that Alfa, Bravo, and Charlie get. For example, if Alfa gets 1, Bravo gets 2, and Charlie get 3, then X = 6. Find IE[X]. (Hint: use the indicator variable and the addition rule.) (b) [lpt] There are two events A and B. 1 means the indicator function. Show that 1,413 = lAnB- (c) [lpt] Suppose A and B are independent in part (a). Show that ]E(1A13) = ]E(1A)IE(13)