Stationary Distribution | Steady State Distribution with Solved Problems

Let {X_n,n ≥ 0} be a Homogeneous Markov Chain (MC) with Transition Probability matrix P. Then if there exists a probability vector π, such that πP = π,
Then   π is called Stationary Distribution or Steady State Distribution or Limiting Probability.

Here,     π  =  (π₁, π₂, π₃,......,π_n ), then  π₁+ π₂+ π₃+......+π_n = 1

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Solved Problems of Limiting Probability

Solved Problem 1: Assume that a computer system is in any one of the three states: busy, idle and under repair respectively. denoted by 0,1,2. Observing its state at 2 pm each day, we get the Transition Probability matrix as:

Find out the third step TPM and also determine the Limiting Probability.

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