A Ticket counter has four (4) systems. The arrival rate of the machine is 3 per hour (Poisson distributed) and it can serve an average of 4 per hour (Poisson distributed). Assuming the repairing capacity is one system a week, the repairing time being exponentially distributed. Find the Probability that the service facility will be idle I. II. Find the probability that there shall be exactly 3 systems to be, and being, repaired Find the expected length of queue (number of machines in the Queue) Find the expected number of machines waiting to be and being, repaired. (number of machines in the system) Find the expected time a machine shall wait in the queue to be repaired, and (Average time in the Queue) Find the expected time that a machine shall spend in the system that is waiting for and getting repaired. (Average time in the system) IV. V. VI.