A Ma r k o v c h a i n X0, X1, X2, ... h a s t h e t r a n s i t i o n p r o b a b i l i t y m a t r i x 1 2 3 (0.7 0.2 0.1) (0 0.6 0.4) (0.5 0 0.5) Th e Ma r k o v c h a i n i s a. E r g o d i c b. T r a n s i e n t c. N o t e r g o d i c d. N o n e o f t h e s e
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A Markov chain is ergodic if it is both irreducible and aperiodic. Irreducibility means that it is possible to reach any state from any other state, either directly or indirectly. In this case, we can see that all states are reachable from any other state, so Show more…
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A Markov chain X0, X1, X2 ... on states 0, 1, 2 has the transition probability matrix 0 1 2 0 0.3 0.2 0.5 P = 1 0.5 0.1 0.4 2 0.5 0.2 0.3 and initial distribution p0 = P(X0 = 0) = 0.2, p1 = P(X0 = 1) = 0.3, and p2 = P(X0 = 2) = 0.5. Determine the following probabilities: (1) P(X0 = 1, X1 = 1, X2 = 0); (2) P(X1 = 1, X2 = 2 | X0 = 2); (3) P(X3 = 0, X4 = 0, X5 = 2 | X2 = 1);
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Find the steady state matrix $X$ of the absorbing Markov chain with matrix of transition probabilities $P$. $$P=\left[\begin{array}{llll} 0.7 & 0 & 0.2 & 0.1 \\ 0.1 & 1 & 0.5 & 0.6 \\ 0 & 0 & 0.2 & 0.2 \\ 0.2 & 0 & 0.1 & 0.1 \end{array}\right]$$
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