Past records indicate that of the five machines that a factory owns, breakdowns occur at random and the average time between the breakdowns is 2 days. Assuming that the repairing capacity of the workman is one machine a day and the repairing time is distributed exponentially, determine the following:

(a) the probability that the service facility will be idle,

(b) the probability of various number of machines (0 through 5) to be, and being repaired,

(c) the expected length of the queue,

(d) the expected number of machines waiting to be, and being repaired,

(e) the expected time that a machine shall wait in the queue to be repaired, and

(f) the expected time a machine shall be idle for reason of waiting to be repaired and being repaired.