Consider a workshop that has five machines and one repairperson. The machines work independently from one another: A machine fails after a time that is exponentially distributed with parameter =0.2 per hour. If a machine is down it is repaired in an Expo() distributed amount of time, where = 0.5 per day. At most one machine can be under repair at any given time. Calculate the fraction of time that the repairperson is idle/ unoccupied in the long run.