2. A Markov chain X0, X1, ... with states 1, 2, 3 has transition probability matrix egin{pmatrix} .4 & 0 & .6 \ .2 & .8 & 0 \ .3 & .3 & .4 end{pmatrix} (a) Give its classes and tell which are recurrent and which are transient. (b) Find P(X2 = 1|X0 = 2). (c) Find the long run proportion of time the chain spends in state 2.
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First, we need to find the transition probability matrix P. We are not given the matrix in the question, so we cannot proceed with the analysis. Assuming we have the transition probability matrix P, we can proceed with the following steps: Show more…
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A Markov chain X0, X1, X2, ... has the transition probability matrix 0 1 2 0 0.3 0.2 0.5 P = 1 0.5 0.1 0.4 2 0.5 0.2 0.3 Every period that the process spends in state 0 incurs a cost of $2. Every period that the process spends in state 1 incurs a cost of $5. Every period that the process spends in state 2 incurs a cost of $3. What is the long run cost per period associated with this Markov chain?
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