The computer center at Rockbottom University has been experiencing computer down time. Let us assume that the trials of an associated Markov process are defined as one-hour periods and that the probability of the system being in a running state or a down state is based on the state of the system in the previous period. Historical data show the following transition probabilities

3. The computer center at Rockbottom University has been experiencing computer down time. Let us assume that the trials of an associated Markov process are defined as one-hour periods and that the probability of the system being in a running state or a down state is based on the state of the system in the previous period. Historical data show the following transition probabilities: From Running Down Running 0.90 0.10 Down 0.30 0.70 TO a. If the system is initially running, what is the probability of the system being down in next hour of operation? b. At a current period, the system is in a down state. After 2 periods of time, what is the probability that the system will be in the state of running? c. What are the steady-state probabilities of system being in the running state and in the dowit state