Let be the transition matrix for a Markov chain with two states. Let be the initial state

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Let
0.5 0.3 P = 0.5 0.7.

be the transition matrix for a Markov chain with two states.

Let
0.5 Xo 0.5

be the initial state vector for the population.

What proportion of the state 1 population will be in state 2 after two steps?

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