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1. A computer is inspected at the end of every hour. It is found to be either working (up) or failed (down). If the computer is found to be up, the probability of its remaining up for the next hour is 0.95. If it is down, the computer is repaired, which may require more than 1 hour. Whenever the computer is down (regardless of how long it has been down), the probability of its still being down 1 hour later is 0.5. The (one-step) transition matrix for this Markov chain is given by P = [0.95 0.05]. 0.5 (a) find the µ₁j (the expected first passage time from state į to state j) for all i and j. (b) Use the results from part (a), to answer the following questions. What is the expected number of hours that the computer will be keep working? What is the expected number of hours that the computer will be working again after it fails?

1. A computer is inspected at the end of every hour. It is found to be either working (up) or failed (down). If the computer is found to be up, the probability of its remaining up for the next hour is 0.95. If it is down, the computer is repaired, which may require more than 1 hour. Whenever the computer is down (regardless of how long it has been down), the probability of its still being down 1 hour later is 0.5. The (one-step) transition matrix for this Markov chain is given by P = [0.95 0.05]. 0.5 (a) find the µ₁j (the expected first passage time from state į to state j) for all i and j. (b) Use the results from part (a), to answer the following questions. What is the expected number of hours that the computer will be keep working? What is the expected number of hours that the computer will be working again after it fails?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. A computer is inspected at the end of every hour. It is found to be either working (up) or failed (down). If the computer is found to be up, the probability of its remaining up for the next hour is 0.95. If it is down, the computer is repaired, which may require more than 1 hour. Whenever the computer is down (regardless of how long it has been down), the probability of its still being down 1 hour later is 0.5. The (one-step) transition matrix for this Markov chain is given by -[0.⁹5 0.05]. P = (a) find the µ¡¡ (the expected first passage time from state i to state j) for all i and j. (b) Use the results from part (a), to answer the following questions. What is the expected number of hours that the computer will be keep working? What is the expected number of hours that the computer will be working again after it fails?
Transcribed Image Text:1. A computer is inspected at the end of every hour. It is found to be either working (up) or failed (down). If the computer is found to be up, the probability of its remaining up for the next hour is 0.95. If it is down, the computer is repaired, which may require more than 1 hour. Whenever the computer is down (regardless of how long it has been down), the probability of its still being down 1 hour later is 0.5. The (one-step) transition matrix for this Markov chain is given by -[0.⁹5 0.05]. P = (a) find the µ¡¡ (the expected first passage time from state i to state j) for all i and j. (b) Use the results from part (a), to answer the following questions. What is the expected number of hours that the computer will be keep working? What is the expected number of hours that the computer will be working again after it fails?
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