Consider the Markov chain consisting of the three states 0, 1, 2 and having transition probability matrix

It is easy to verify that this Markov chain is irreducible. For example, it is possible to go from state 0 to state 2 since 0 → 1 → 2 That is, one way of getting from state 0 to state 2 is to go from state 0 to state 1 (with probability 12 ) and then go from state 1 to state 2 (with probability 14 ).

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227T 21227 17 23 O = d