Question: Question 3. [12 Marks). Consider a Markov process {X(t) }to with state space S = {0, 1, 2, 3 } and Q-matrix, or genarator, -90

Question 3. [12 Marks). Consider a Markov process {X(t) }to with

Question 3. [12 Marks). Consider a Markov process {X(t) }to with state space S = {0, 1, 2, 3 } and Q-matrix, or genarator, -90 2 O O - 91 4 Q = 4 - 92 2 O O O -93 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 To associated with Q. (c) The proportion of time the process spends in state 3 in the long run. (d) The expected return time, m2, for state 2. (e) The transition matrix R of the embedded chain. (f) A stationary distribution TR of the embedded chain. Is the stationary distribution TR that you found unique? Explain your reasoning

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