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 To Down Running 0.90 0.10 Down 0.30 0.70 a. If the system is initially running, what is the probability of the system being down in the next hour of operation? b. What are the steady-state probabilities of the system being in the running state and in the down state?
Solution: a) The probability of system being down in next hour of operation is 0.10. (From chart mentioned in the question)