A Markov chain has state space (mathbf{Z}={0,1,2,3}) and transition matrix [mathbf{P}=left(begin{array}{cccc} 0 & 0 & 1 &

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A Markov chain has state space \(\mathbf{Z}=\{0,1,2,3\}\) and transition matrix

\[\mathbf{P}=\left(\begin{array}{cccc} 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ 0.4 & 0.6 & 0 & 0 \\ 0.1 & 0.4 & 0.2 & 0.3 \end{array}\right)\]

Determine the classes of essential and inessential states.

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