A Markov chain with the state space S12 has the following tr

A Markov chain with the state space S={1,2} has the following transition matrix, limiting transition matrix, limiting distribution etc...

A Markov chain with the state space S = {1,2} has the following transition probability matrix, Write down P^n from Question 8 of Assignment 2, and then find the limiting transition matrix. Find the limiting distribution of the Markov chain using global balance equations. From (b), find the long-run proportion of the chain being in state 1 and 2. Explain. From (b), find the stationary distribution of the chain. Explain.

Solution

Given S={1,2} is the state space of a Markov chain

Following transition matrix, limiting transition matrix, limiting distribution

We here take given space state s={1,2}

With this using modes transition matrix is gives transition only the another limiting that will take point about limiting point the last is distribution matrix

This will distribution with a state space s={1,2}.