8. Consider a Markov chain with states 1, 2, 3, 4, 5, 6 and a transition...

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8. Consider a Markov chain with states 1, 2, 3, 4, 5, 6 and a transition probability matrix 1/5 2/5 1/5 0 0 1/5 1/10 4/10 4/10 0 P = 0 0 0 0 0 0 0 0 2/5 3/5 0 3/4 1/4 0 0 0 1/10 0 0 0 0 1/2 1/2 0 1/3 2/3 a. Give the classes and tell which are recurrent and which are transient. b. Find limno P2- c. Find limn→∞ P5,6- d. If Xo = 1, find the mean number of transitions until either state 3 or 4 is entered.] 8. Consider a Markov chain with states 1, 2, 3, 4, 5, 6 and a transition probability matrix 1/5 2/5 1/5 0 0 1/5 1/10 4/10 4/10 0 P = 0 0 0 0 0 0 0 0 2/5 3/5 0 3/4 1/4 0 0 0 1/10 0 0 0 0 1/2 1/2 0 1/3 2/3 a. Give the classes and tell which are recurrent and which are transient. b. Find limno P2- c. Find limn→∞ P5,6- d. If Xo = 1, find the mean number of transitions until either state 3 or 4 is entered.]