Consider the following transition matrices. \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \quad \begin{pmatrix} .5 & 0 & .5 \\ 0 & .5 & .5 \\ .5 & .5 & 0 \end{pmatrix} \quad \begin{pmatrix} .5 & .3 & .1 & .1 \\ 0 & 0 & .4 & .6 \\ .4 & .2 & .2 & .2 \\ 0 & 0 & .5 & .5 \end{pmatrix} (1) For each matrix, construct a markov diagram. Then determine which states are\\ recursive/transient and periodic/aperiodic. (2) Which of these matrices are ergodic? If a matrix is not ergodic, explain why.
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First, let's construct the Markov diagram for the given transition matrix. Show more…
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