8. [5+7 pts] A single repair person is in charge of repair of two different machines. Suppose the amount of time each machine works before breaking down is exponentially distributed with rate A and the amount it takes to repair either machine is exponentially distributed with rate ,u. When a machine breaks down, if the repair person is free they start the repair of it immediately, else if they are busy with the other machine, then the repair begins only after repair of the other machine is nished. (a) Dene a continuous time Markov chain representing the number of working machines at time t Z 0. (b) Find the long-run average of working machines