Problem 16-03 (Algorithmic) The computer center at Rockbottom University has been experiencing computer downtime. 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: To From Running Down Running 0.70 0,20 Down 0.30 0.80 a. If the system is initially running, what is the probability of the system being down in the next hour of operation? If required, round your answers to two decimal places. The probability of the system is b. What are the steady-state probabilities of the system being in the running state and in the down state? required, round your answers to two decimal places. 11 = Problem 16-05 (Algorithmic) A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.9 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.7. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes. a. Assume that you are a motorist entering the traffic system and receive a radio report of a traffic delay. What is the probability that for the next 60 minutes (two time periods) the system will be in the delay state? Note that this result is the probability of being in the delay state for two consecutive periods. If required, round your answer to three decimal places. b. What is the probability that in the long run the traffic will not be in the delay state? If required, round your answers to three decimal places. Problem 16-03 (Algorithmic) The computer center at Rockbottom University has been experiencing computer downtime. 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: To From Running Down Running 0.70 0,20 Down 0.30 0.80 a. If the system is initially running, what is the probability of the system being down in the next hour of operation? If required, round your answers to two decimal places. The probability of the system is b. What are the steady-state probabilities of the system being in the running state and in the down state? required, round your answers to two decimal places. 11 = Problem 16-05 (Algorithmic) A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.9 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.7. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes. a. Assume that you are a motorist entering the traffic system and receive a radio report of a traffic delay. What is the probability that for the next 60 minutes (two time periods) the system will be in the delay state? Note that this result is the probability of being in the delay state for two consecutive periods. If required, round your answer to three decimal places. b. What is the probability that in the long run the traffic will not be in the delay state? If required, round your answers to three decimal places