Question 5 (15 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) (4 pts) What is the expected length of the queue at the McDonald's? (b) Bobby just arrive at the McDonald's. (4 pts) What is the probability that he sees 2 people queueing? (4 pts) What is the probability that he spends less than 2 minutes but more than 1 minute in the McDonald's? 2 (3 pts) What is the expected amount of time he spends in the queue? Question 5 (15 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) (4 pts) What is the expected length of the queue at the McDonald's? (b) Bobby just arrive at the McDonald's. (4 pts) What is the probability that he sees 2 people queueing? (4 pts) What is the probability that he spends less than 2 minutes but more than 1 minute in the McDonald's? 2 (3 pts) What is the expected amount of time he spends in the queue