Probability

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? 19 . (3 pts) What is the expected amount of time he spends in the queue