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4. The status of a processing machine (M) in company A can be divided into: good (state 0 ), usable (state 1), faulty (state 2) and other states. The following table shows the machine for a certain hour and times an hour The one-step transition matrix of its state evolution. It is worth noting that when the machine is faulty After maintenance, the probability of returning to a good state in the next hour is (1/5), the probability of returning to a usable state is ( 3/5), and the probability of still being in a faulty state is (1/5). (a) steady-state probabilities. ( 10 Points) (b) If the machine is in good condition, it can produce 10 products per hour; if the machine is available, it can produce 6 products per hour, if the machine is in failure state, it cannot produce products. In the long run, how many products can the machine produce per hour? (10 Points) (C) In the long run, how many hours does it take on average for the machine to go from a good state to failure? And in the long run, how many hours does it take on average for the machine to return to a good state