1. A computer center has an old computer which seems to be developing too many minor problems to go unnoticed. The center's director has instituted a study of its operation and collected data over a considerable period of time. At every minute the state of computer has been noted down as working or not working (if it is not working at one observation point, repair is initiated immediately, which may take one or more observation periods). The analysis of such data over a long period of time has revealed the following pattern. If the computer is not working at an observation epoch, the probability that it will be still under repair at the next observation epoch (after 1min ) is 0.8. On the other hand, if it is working at an observation epoch, the probability is 0.95 that it will continue to be working at the next observation epoch. Assuming that these probabilities of changes of state remain constant each time, the director would like to get answers for the following questions: - Given that the computer was working at 8:00 A.M., what are the chances that it would be working after 15min ? What are the chances it would not be working after one hour? - Suppose the computer is observed not working at an observation epoch. How long is the repair expected to continue? If the state of the computer is modeled as a stochastic process Xn with states 0 (working) and 1 (not working), the transition probability matrix can be given as P=(0.950.200.050.80)