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Question: 2 a markov chain with a finite number of states...

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2. A Markov Chain with a finite number of states is said to be regular if there exists a non negative integer n such that for any i, J E S, Fini > 0 for any n-มิ. (a) Prove that a regular Markov Chain is irreducible. (b) Prove that a regular Markov Chain is aperiodic (c) Prove that if a Markov Chain is irreducible and there exists k E S such that Pk0 then it is regular (d) Find an example of an irreducible Markov chain which is not regular

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