3. Suppose students come to my office hours following a Poisson process with rate 5 per hour. The average time I clarify their questions is 10 minutes and my service time follows an exponential distribution (Solve this question manually).

a. What is the probability that you will see me idle during office hours?

b. On average, how many students are waiting for their questions clarified?

c. On average, what is the total length of time (from arrival to departure) students will spend at my office?

d. What is the probability that a student has to wait for service?