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.
(a) Construct the (one-step) transition matrix for this Markov chain.
(b) Use the approach described in Sec. 29.6 to find the µij (the expected first passage time from state i to state j) for all i and j.