Question 3 (25 pts). NUS students come by a McDonald's according to the Poisson process with rate 6 people per minutes. The McDonald's has only one counter, which serves the students by dishing out burgers. The time to dish out a burger [in minute) follows Exp(12), independent of the arrival. NUS students, being rather civilized and patient, join a single queue if the counter is busy with an order. Due to a circuit breaker, a students immediately leaves the McDonald's after getting his / her burger. Suppose the McDonald's has been open for a long time. (a) (5 pts) What is the expected length of the queue at the McDonald's? (b) Bobby just arrive at the McDonald's. a (8 pts) What is the probability that he sees 2 people queueing? I (7 pts) What is the probability that he spends less than 2 minutes but more than 1 minute in the McDonald's? a (5 pts) What is the expected amount of time he spends in the queue