MATH3801 Probability & Stochastic Proc

5. A system consists of three machines and two repairmen. At most two machines can operate at any time. The amount of time that an operating machine works before breaking down is exponentially distributed with mean 5 hours. The amount of time that it takes a single repairman to x a machine is exponentially distributed with mean 4 hours. Only one repairman can work on a failed machine at any given time. Let X(t) be the number of machines in working order at time t. a) Calculate the long-run probability distribution of X(t). b) In the long run, what fraction of time are both repairmen busy? c) If an operating machine produces 100 units of output per hour, what is the long run output per hour of the system