Question: Consider a circular random walk in which six points 1, 2, 3, 4, 5, 6 are placed on a circle in clockwise order. Suppose that

Consider a circular random walk in which six points 1, 2, 3, 4, 5, 6 are placed on a
circle in clockwise order. Suppose that one-step transitions are possible only from one point
to adjacent points with equal probabilities.

(a) Draw a transition diagram and write a matrix for this Markov chain.
(b) Starting from 3, find the probability that in 5 transitions, the Markov chain enters 2.
(c) What are the expected numbers of visits from 3 to all the state (including 3 itself) after
6 transitions?
(d) What is the probability that state 6 has not been visited after 3 transitions.

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