Find the stationary distribution for the Ehrenfest Markov Chain.

Data from in stationary distribution

If we have an ergodic Markov Chain, we know that each state will be visited infinitely often. However, this implies that over the long run, the number of times it will be in a given state may be obtained.

A vector χ is called the stationary distribution of an ergodic Markov Chain if

A stationary distribution χ is a (left) eigenvector of the TPM whose associated eigenvalue is equal to one. For an ergodic Markov Chain, the next program gives us the stationary distribution.

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x; ≥ 0, ` =; = 1, 元P = x.