A Markov chain (left{X_{0}, X_{1}, ldots ight}) has state space (mathbf{Z}={0,1,2}) and transition matrix [mathbf{P}=left(begin{array}{ccc} 0 &
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A Markov chain \(\left\{X_{0}, X_{1}, \ldots\right\}\) has state space \(\mathbf{Z}=\{0,1,2\}\) and transition matrix
\[\mathbf{P}=\left(\begin{array}{ccc} 0 & 0.4 & 0.6 \\ 0.8 & 0 & 0.2 \\ 0.5 & 0.5 & 0 \end{array}\right)\]
(1) Given the initial distribution \(P\left(X_{0}=0\right)=P\left(X_{0}=1\right)=0.4\) and \(P\left(X_{0}=2\right)=0.2\), determine \(P\left(X_{3}=2\right)\).
(2) Draw the corresponding transition graph.
(3) Determine the stationary distribution.
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Related Book For
Applied Probability And Stochastic Processes
ISBN: 9780367658496
2nd Edition
Authors: Frank Beichelt
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