Suppose a Markov chain with unique positive stationary distribution Ï starts at state i. The expected number

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Suppose a Markov chain with unique positive stationary distribution π starts at state i. The expected number of steps until the chain revisits i is called the expected return time of state i.We state without proof that the expected return time of state i is equal to 1/πi. Find the expected return time of the center vertex in the lollipop graph of Figure 10.14.

FIGURE 10.14: Lollipop graph on nine vertices.

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