Consider a Markov chain with two states and transition probability matrix P = (0 11 0). Find thestationary distribution of the chain

To find the stationary distribution of the Markov chain, we need to solve the equation πP = π, where π is the stationary distribution and P is the transition probability matrix.

Given that the Markov chain has two states, let's denote the stationary distribution as π = [π1, π2]. The transition probability matrix is given as P = [0 1; 1 0].

Now, let's set up the equation πP = π:

[π1, π2] * [0 1; 1 0] = [π1, π2]

This equation can be expanded as:

π1 * 0 + π2 * 1 = π1 π1 * 1 + π2 * 0 = π2

Simplifying these equations, we get:

π2 = π1 π1 = π2

Since π1 = π2, we can choose any value for π1 and set π2 equal to that value. Let's choose π1 = 1.

Therefore, the stationary distribution of the Markov chain is π = [1, 1].