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Subject:  Finite Math

Steady state of a two-state Markov chain

Iterate the distribution and solve for the steady-state vector.

Answer p5 = (0.57247, 0.42753); π = (0.571429, 0.428571)

Solution

  1. Transition matrix 2×2 [0.7, 0.3; 0.4, 0.6]
  2. Initial distribution p₀ = (1, 0)
  3. Step 1 p1 = (0.7, 0.3)
  4. Step 2 p2 = (0.61, 0.39)
  5. Step 3 p3 = (0.583, 0.417)
  6. Step 4 p4 = (0.5749, 0.4251)
  7. Step 5 p5 = (0.57247, 0.42753)
  8. Steady-state distribution π = (0.571429, 0.428571)

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