Question 10.5.P.1: Consider a Markov chain on {1, 2, 3, 4} with transition matr...
Consider a Markov chain on {1, 2, 3, 4} with transition matrix
P=\left[\begin{array}{cccc}1 & 1 / 2 & 0 & 0 \\0 & 1 / 6 & 1 / 2 & 0 \\0 & 1 / 3 & 1 / 6 & 0 \\0 & 0 & 1 / 3 & 1\end{array}\right].
a. If the Markov chain starts at state 2, find the expected number of steps before the chain is absorbed.
b. If the Markov chain starts at state 2, find the probability that the chain is absorbed at state 1.
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