Suppose that a production process changes state according to a Markov process whose transition probability matrix...

  

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Suppose that a production process changes state according to a Markov process whose transition probability matrix is given by P = 0 0 0.3 1 0.5 2 0.2 30.1 1 0.5 0 0.2 0.2 0.2 0.1 0.3 0.4 0.1 0.2 0.4 0.3 2 3 119 It is known that ₁ 379 (a) Determine the limiting probabilities лo and 73. (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? = 0.3140 and 72 = 3= 0.2137. Suppose that a production process changes state according to a Markov process whose transition probability matrix is given by P = 0 0 0.3 1 0.5 2 0.2 30.1 1 0.5 0 0.2 0.2 0.2 0.1 0.3 0.4 0.1 0.2 0.4 0.3 2 3 119 It is known that ₁ 379 (a) Determine the limiting probabilities лo and 73. (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? = 0.3140 and 72 = 3= 0.2137.

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