Question

Consider a random walk among 3 points labelled {a,b, c}. Each minute, she makes a move, and her movements are

dictated by the following constraints that follows:

(i) If (current position) equals (previous-minute position), then go to any one of the other two positions with equal probability;

(ii) If (current position) does not equal (previous-minute position), then continue to stay in current position during the next minute.

Please answer the following questions:

(a). Determine the state-space, such that the system evolution can be described by a Discrete Time Markov Chain. Justify your answer. Draw the state transition diagram, with the states labeled and the edges labeled with the transition probabilities.

(b). Is the Markov chain irreducible and aperiodic?

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