Question: Suppose you are standing along an isolated country road (with obviously nothing else better to do), and cars pass by at an average (Poisson) rate of 5 per hour.

(a) What is the probability that in any one hour less than 3 cars pass by?

(b) What is the probability that in any one 6-hour period exactly 40 cars pass by?

(c) How long, on the average, once you start standing there, should you expect to wait before the first car goes by?

(d) What is the probability that you have to wait longer than your answer to part (c)?

(e) How long on the average, once you start standing there, should you expect to wait until the first three cars go by?

(f) What is the probability that you have to wait longer than your answer to part (e)?