Question: Question 3. [12 Marks]. Consider a Markov process {X (t)}t20 with state space S = {0, 1, 2, 3} and Q-matrix, or genarator, 0 0

Question 3. [12 Marks]. Consider a Markov process {X (t)}t20 with state space S = {0, 1, 2, 3} and Q-matrix, or genarator, 0 0 1 q3 Determine the following quantities. (a) The expected holding time of each state (i.e. the expected amount of time spent in each state before a jump). (b) The stationary distribution aQ associated with Q. (c) The proportion of time the process spends in state 3 in the long run. ((1) The expected return time, 7122, for state 2. (e) The transition matrix R of the embedded chain. (1') A stationary distribution 7TB of the embedded chain. Is the stationary distribution 77;; that you found unique? Explain your reasoning

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