Problem 4 (from the supplementary problems to Introduction to Probability, 1315 ed.) (a) Shuttles depart from New York to Boston every hour on the hour. Passengers arrive according to a Poisson process of rate A per hour. Find the expected number of passengers on a shuttle. (Ignore issues of limited seating.) (b) Now, and for the rest of this problem, suppose that the shuttles are not operating on a deterministic schedule, but rather their interdeparture times are exponentially distributed with rate it per hour, and independent of the process of passenger arrivals. Find the PMF of the number shuttle departures in one hour. (c) Let us dene an \"event\" in the airport to be either the arrival of a passenger, or the departure of a plane. Find the expected number of \"events\" that occur in one hour. (d) If a passenger arrives at the gate, and sees 2}. people waiting, nd his/ her expected time to wait until the next shuttle. (e) Find the PMF of the number of people on a shuttle