1. Suppose that for a Markov Chain with 3 states the following 2 step and 3 step transition probability matrices are obtained. Then P(X105=2 | X100=2) is ? P^{(2)} = egin{matrix} 1 \ 2 \ 3 end{matrix} egin{bmatrix} 0.28 & 0.48 & 0.24 \ 0.21 & 0.58 & 0.21 \ 0.23 & 0.50 & 0.27 end{bmatrix} P^{(3)} = egin{matrix} 1 \ 2 \ 3 end{matrix} egin{bmatrix} 0.224 & 0.560 & 0.216 \ 0.237 & 0.526 & 0.237 \ 0.223 & 0.546 & 0.231 end{bmatrix}
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The rows represent the current state and the columns represent the future state. The question asks for the probability of transitioning from state 2 to state 2 in 5 steps, given that we start in state 2. We don't have a 5-step transition matrix, but we can use Show more…
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