Answer Happy

Problem 4 (30 points) Three machines operate together on a manufacturing floor, and each day there is a possibility that any of the machines may fail. The probability of their failure depends upon how many other machines are still in operation. The number of machines in operation at the beginning of each day is represented by the state values of 0, 1, 2, 3 and the corresponding state transition probability matrix is 1 0 0 0 0.3 0.7 0 0 P 0.2 0.3 0.5 0 [0.1 0.1 0.1 0.7] Let X. = X[n] denote this discrete Markov chain. (a) Draw the state transition diagram (5 points) (b) Determine and state the number of classes and find the mean recurrence time of state 0 (10 points) (e) How many days will pass before the probability of all three machines failing is greater than 0.8. You will need a computer to find the solution (15 points) m