Problem 10 Consider the Markov chain specified in Fig. 7.25. 0.5 0.4 0.4 0.4 شعر عرايا 0.5 0.1 0.2 0.2 3 0.5 0.6 0.7 0.2

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Problem 10 Consider the Markov chain specified in Fig. 7.25. 0.5 0.4 0.4 0.4 شعر عرايا 0.5 0.1 0.2 0.2 3 0.5 0.6 0.7 0.2 0.3 Figure 7.25: Transition probability graph for Problem 30, (a) Identify the transient and recurrent states. Also, determine the recurrent classes and indicate which ones, if any are periodic. (b) Do there exist steady-state probabilities given that the process starts in state 1? If so, what are they? (c) Do there exist steady-state probabilities given that the process starts in state 6? If so, what are they? (a) Assume that the process starts in state 1 but we begin observing it after it reaches steady-state. (i) Find the probability that the state increases by one during the first transi- tion we observe. (ii) Find the conditional probability that the process was in state 2 when we started observing it, given that the state increased by one during the first transition that we observed. (iii) Find the probability that the state increased by one during the first change of state that we observed. (e) Assume that the process starts in state 4. (1) For each recurrent class, determine the probability that we eventually reach that class.