In a Poisson process, the probability that exactly one event will occur in any given hour is 3e-3.
(a) What is the probability that exactly two events will occur in any 20-minute period?
(b) Suppose you start observing the process at some point of time. What is the probability that it will be less than 10 minutes until an event occurs?
(c) Take a unit of time to be 1 hour. Starting at time 0, find the expectation and variance of the time of the fifth occurrence.