The life of a car is a random variable with distribution F An individual has a policy of trading in his car either when it fails or reaches the age of A. Let R(A) denote the resale value of an A-year-old car. There is no resale value of a failed car Let C, denote the cost of a new car and suppose that an additional cost C is incurred whenever the car fails.

(a) Say that a cycle begins each time a new car is purchased Compute the long-run average cost per unit time

(b) Say that a cycle begins each time a car in use fails Compute the long-run average cost per unit time Note. In both

(a) and

(b) you are expected to compute the ratio of the expected cost incurred in a cycle to the expected time of a cycle The answer should, of course, be the same in both parts