Question 1 Winston 172 Problem 3 Modified A company has two

Question 1. [Winston 17.2 Problem 3 Modified] A company has two machines. During any day, each machine that is working at the beginning of the day has a 1/3 chance of breaking down. If a machine breaks down during the day, it is sent to a repair facility. It takes either a full day to fix the machine, with a probability of 3/5, or two full days with a probability of 2/5. (Thus, if a machine breaks down during day 3, it will be working at the beginning of day 5 with 3/5 probability or at the beginning of day 6 with 2/5 probability.)

(a) Define the state, X, for the Markov chain model and write all the values X can take, i.e., the state set S.

(b) Write the transition probability matrix.

(c) Draw the Markov chain state transition diagram

Solution