Question

A Markov chain model for a copy machine has three states: working, broken and fixable, broken and unfixable. If it is working, there is 69.9% chance it will be working tomorrow and 0.1% chance it will be broken and unfixable tomorrow. If it broken and fixable today, there is a 49% chance it will be working tomorrow and 0.2% chance it will be unfixable tomorrow. Unfixable is, of course unfixable, so the probability that an unfixable machine is unfixable tomorrow is 1 and the probability of its being anything other than unfixable is 0. Assume a day as the time step.

a) Draw a state diagram for this scenario. Categorize the sates as absorbing and nonabsorbing.

b) Formulate the transition matrix. Label the states so that the identity.

C.) Compute the fundamental matrix and interpret the results. How long will this machine last? How much of this time will it be working, and how much of that time will it be under repair (broken and fixable)?

Answer 1

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