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Linear AlgebraEasyMarkov Chains & Long-Run Behavior

Markov Chains & Long-Run Behavior · Easy problem

A two-state Markov chain has transition matrix M=(0.90.20.10.8)M = \begin{pmatrix} 0.9 & 0.2 \\ 0.1 & 0.8 \end{pmatrix}, where MijM_{ij} is the probability of moving to state ii from state jj. The starting distribution is x0=(0.50.5)\mathbf x_0 = \begin{pmatrix} 0.5 \\ 0.5 \end{pmatrix}. What is the probability of being in state 1 after one step? Express your answer as a decimal.