A repairman maintains 4 machines. Each time a machine breaks he repairs the machine.
The machines are at a distance of 2 units from one another in a serial arrangement. At
any time instance only one machine may require repair and this happens with a probability
0.02 during a single shift. The repairman can repair all 4 machines if needed in a single
shift. No machine can break more than once in a shift. The repairman is located at a
station at machine nr. 1. After repairing one machine he returns to his station because he
needs to see if a machine requires repair.
a. What is the random variable of interest?
b. Find the density of the total distance covered by the repairman in a single shift.
c. What is the expected total distance covered by the repairman in a single shift?
