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

Consider a circular random walk in which six points 1, 2, 3, 4, 5, 6 are placed, in a clockwise order, on a circle. Suppose that one-step transitions are possible only from a point to its adjacent points with equal probabilities. Starting from 1, (a) find the probability that in 4 transitions the Markov chain returns to 1; (b) find the probability that in 5 transitions the Markov chain enters to an adjacent point of 1, namely, to 2 or 6.

Consider a circular random walk in which six points 1, 2, 3, 4. 5, 6 are placed, in a clockwise order, on a circle. Suppose that one-step transitions are possible only from a point to its adjacent points with equal probabilities. Starting from 1, (a) find the probability that in 4 transitions the Markov chain returns to 1; (b) find the probability that in 5 transitions the Markov chain enters to an adjacent point of 1. namely, to 2 or 6

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