E5.2. Consider a Markov chain with state space S = {1,2,3,4,5, 6} and transition matrix 1 0 0 0 0 0 1| | 0 0 0 P = 0 0 0 3 00 0 0를 0 0 0 0 (a) Draw the transition graph of this chain. (b) Show that state 1 is absorbing and conclude that it is positive re- current. (c) Show that states 2 and 3 are transient. (d) Verify that states 4, 5 and 6 are positive recurrent.

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