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?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
Related questions
Question
![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 歭 (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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9013aac4-319f-4674-a905-071289bd1226%2F20fa1502-a2cd-49b6-ade7-04ad82a5fa9e%2Fvrbph8z_processed.png&w=3840&q=75)
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 歭 (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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