Amanufacturer has a machine that if it ran all day today has a probability of 0.25 of breaking down sometime during the day tomorrow. when the machine breaks down, it goes offline for the remainder of the day and then a technician will spend the next day (after the breakdown) repairing it. a newly repaired machine only has a probability of 0.15 of breaking down sometime tomorrow a. identify the assumptions that allow us to formulate the evolution of status of the machines as a markov chain (2 points) formulate the evolution of the status of the machine at the end of the day as a markov chain by identifying the three possible states at the end of the day, and providing the transition probabilities between these states. (5 points) b. c. determine the expected first passage times hiy for all states i andj. you must provide the set of equations used to calculate hy (9 points) use your results obtained in part c to identify the expected number of full days that the machine will remain operational before the next bre akdown after a repair is completed. (5 points) the machine currently ran all day today. using your results from c to determine the expected number of full days that the machine will remain operational before the next breakdown. (3 points) suppose that the machine has run 7 straight days (including running all day today), how does the expected number of days hereafter until the next breakdown different from your answer in part e. justify your reasoning behind your answer.