Stationary distribution of a two-state chain

MediumProbability Stochastic Processes~4m

A Markov chain on states $\{A, B\}$ has $P(A\to B)=0.3$ and $P(B\to A)=0.6$ . What fraction of the time is spent in state $A$ in the long run? (to 3 decimals)

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Set the flows between states equal at stationarity.
Solve $\pi_A\cdot 0.3 = \pi_B\cdot 0.6$ with $\pi_A+\pi_B=1$ .

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0.6667 (± 0.005)

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Stationary distribution of a two-state chain

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