Question

Solve the following exercise:

A computer is inspected at the end every hour. The computer may be either working (up) or failed (down). If the computer is to be found up, the probability of remaining up for the next hour is 0.90. 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), the probability of its still being down one hour later is 0.35.

A) Construct the one-step transition matrix for this Markov chain. (Explain)

B) Construct the state transition diagram. (Explain)

C) The computer is inspected now and it is found up. What is the probability that it is down in two hours? (Explain)

D) Given that the computer is up, what is the expected time it will be down for the first time? (Explain)

Answer 1