1. Consider two machines that are maintained by a single repairman. Each machine functions for an exponentially distributed amount of time with rate A before it fails. The repair times for each unit are exponential with rate p. Formulate a Markov chain model for this situation with state space indicating the number of machines that are in the repair shop: S={0,1,2}. Notice that you move from 0 to 1 if one of the two machines breaks down. You move from 1 to 0 when the machine in the repair room is repaired. 2. Same as above but now machines are repaired in the order in which they fail. Each machine functions for an exponentially distributed amount of time with rate Ai before it fails. The repair times for each unit are exponential with rate Hi The state space has nodes that are keep track of the machine that is at the repair shop (in case there is only one) and keeps track of which machine is worked on in case there are two machines at the repair shop. That is the state space is S=(O, 1, 2, 12, 21}. Formulate a Markov chain model for this situation