3. Determine the limiting distribution if 0.6 0.3 0.1 a) T = 0.3 0.3 0.4 0.4 0.1 0.5 0.1 0.1 0.8 b) T=0.2 0.2 0.6 0.3 0.3 0.4 0.3 0.2 0.5 c) T=0.5 0.1 0.4 0.5 0.2 0.3 0.7 0.2 0.1 d) T = 0 0.4 0.6 0.5 0 0.5 4. Suppose that a production process changes state according to a Markov process whose transition probability matrix is given by 0.3 0.5 0 0.2 0.5 0.2 0.2 0.1 T = 0.2 0.3 0.4 0.1 0.2 0.4 0.1 0.3 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?