Question: 3.4.9 Consider the Markov chain whose transition probability matrix is given by Starting in state 1, determine the probability that the process is absorbed into

3.4.9 Consider the Markov chain whose transition probability matrix is given by

P= 0 1 2 3 01 100 1 0.1 0.2 0.5 0.2

Starting in state 1, determine the probability that the process is absorbed into state 0. Compare this with the .1;0/th entry in the matrix powers P2;P4;P8, and P16.

P= 0 1 2 3 01 100 1 0.1 0.2 0.5 0.2 2 0.1 0.2 0.6 0.1 3 0 000 01

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