Work out markov chain steady state instantly with clear inputs, formula shown and shareable results.
A two-state Markov chain with transition probabilities b (leaving state 1) and c (leaving state 2) has steady state π₁ = c/(b + c). The chain forgets its starting point at a rate governed by the second eigenvalue a + d − 1.
Two-state steady state
π₁ = c / (b + c), π₂ = b / (b + c)
b = 0.3 and c = 0.4, so the steady state is π₁ = 4/7 ≈ 0.5714 and π₂ = 3/7 ≈ 0.4286.
Only in the short run. For an irreducible aperiodic chain the long-run distribution is independent of where you start.