Consider the machine reliability model in Example 2.2 with one machine.

The Depend-On-Us company manufactures a machine that is either up or down. If it is up at the beginning of a day, then it is up at the beginning of the next day with probability .98 (regardless of the history of the machine), or it fails with probability .02. Once the machine goes down, the company sends a repair person to repair it. If the machine is down at the beginning

of a day, it is down at the beginning of the next day with probability .03 (regardless of the history of the machine), or the repair is completed and the machine is up with probability .97. A repaired machine is as good as new.

Suppose the machine is up at the beginning of day 0. Compute the probability that the state of the machine at the beginning of the next three days is up, down, down, in that order.

2.8. Consider the machine reliability model in Example 2.2 with one machine. Sup pose the machine is up at the beginning of day 0. Compute the probability that the state of the mlachine at the beginning of the next three days is up, down, down, in that order. Example 2.2. (Machine Reliability). The Depend-On-Us company manufactures a machine that is either up or down. If it is up at the beginning of a day, then it is up at the beginning of the next day with probability .98 (regardless of the history of the machine), or it fails with probability .02. Once the machine goes down, the company sends a repair person to repair it. If the machine is down at the beginning of a day, it is down at the beginning of the next day with probability .03 (regardless of the history of the machine), or the repair is completed and the machine is up with probability .97. A repaired machine is as good as new. Model the evolution of the