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solve it fast 1. You may use computer to help you for this; the inverse is doable by hand though. Consider the Markov chain shown

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1. You may use computer to help you for this; the inverse is doable by hand though. Consider the Markov chain shown in Figure 1. 1/2 1/8 1/8 1/4 1/2 1/4 1/2 2 1 1/8 1/4 1/8 2/3 1/3 1/8 1/8 1/2 5 1/2 Figure 1: Problem 1 (a) Find all communication classes and classify as recurrent or transient. (b) Is the Markov chain regular? What is the period of state 3

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