Question

Question 1) (50 points) A computer is inspected at the end of every minute. It is found to be either working (up) or failed (down). If the computer is found to be working, the probability of it remaining up for the next minute is 0.80. Whenever the computer is down, the probability of it still being down one minute later is 0.20. (a) Define Xn, and write down the state space S b) In this real life situation, the Markov assumption is 100 % correct. Explain why? c) Give a reason why the stationarity assumption may be problematic in modelling the computer's behavior d) Draw the transition diagram and write down P e)) Suppose that computer is found to be working at the end of first minute. What is the probability that it will be down for two consequative inspections, and working on the third inspection? f)Given at the computer is working at the end of twelveth minute, what is the probability that it will be down at the end of 14th minute?

Answer 1

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