2.3. Suppose that a production process changes state according to a Markov process whose transition probability matrix is given by

(a) Determine the limiting distribution for the process.

(b) Suppose that states 0 and 1 are "in-control," while states 2 and 3 are deemed "out-of-control." In the long run, what fraction of time is the process out-of-control?

(c) In the long run, what fraction of transitions are from an in-control state to an out-of-control state?

0 1 2 3 0 0.2 0.2 0.4 0.2 1 0.5 0.2 0.2 0.1 P = 2 0.2 0.3 0.4 0.1 3 0.1 0.2 0.4 0.3