A division within a transportation company is responsible for performing maintenance on the fleet of trucks used by the company. Trucks in need of repair arrive to the maintenance division according to a Poisson process having a rate of 0.3 trucks per hour.
Suppose we begin observing the maintenance division at some point in time.
(a) What is the probability that it is at least 2 hours until the first truck arrives?
(b) On average, how long would you expect it to be until the first truck arrives?
(c) What is the probability that the third truck arrives within 15 minutes of the second truck?