A two-step transition

MediumStochastic Processes~3m

A Markov chain has transition matrix $\begin{pmatrix}0.9&0.1\\0.5&0.5\end{pmatrix}$ (states A, B). Starting in A, what is the probability of being in A after 2 steps? Give a decimal to two places.

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This is the (A,A) entry of $P^2$ .
Sum over the intermediate state.

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0.86

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A two-step transition

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