4. A factory has two machines and a repair crew. Assume that the probability of any one machine breaking down in a given

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4 A Factory Has Two Machines And A Repair Crew Assume That The Probability Of Any One Machine Breaking Down In A Given 1 (43.92 KiB) Viewed 32 times

4. A factory has two machines and a repair crew. Assume that the probability of any one machine breaking down in a given day is a, and that the machines are independent of each other. Assume that if the repair crew is working on a machine, the prob- ability that they will complete the repair on one more day is 3. The repair crew can work on two machines at the same time, but whether either one is completed or not are independent of each other. For simplicity ignore the possibility of a repair completion or breakdown taking place except at the end of the day. • Let Xn be the random variable for the number of machines in op- eration at the end of the nth day. Assume {X₂} can be described by a Markov chain (a) Write down the one step transition matrix P (b) If the system starts out with both machines operating, what is the probability that both will be operating two days later.