Three blue and three green balls are distributed in two urns in such a way that each urn contains three balls. At each step, we randomly swap a ball from each urn. At any given step, the system is in of the four states {0, 1, 2,3} corresponding to the number of blue balls in the first urn. In other words, the system is in state i if the first urn has i blue balls, where i = 0,1,2,3. (a) Define a Markov chain to describe the number of blue balls in the first urn and write the corresponding transition probability matrix. (b) Find the Stationary distribution corresponding to the Markov chain. What is the limiting probability of having no green balls in the first urn? Three blue and three green balls are distributed in two urns in such a way that each urn contains three balls. At each step, we randomly swap a ball from each urn. At any given step, the system is in of the four states {0, 1, 2,3} corresponding to the number of blue balls in the first urn. In other words, the system is in state i if the first urn has i blue balls, where i = 0,1,2,3. (a) Define a Markov chain to describe the number of blue balls in the first urn and write the corresponding transition probability matrix. (b) Find the Stationary distribution corresponding to the Markov chain. What is the limiting probability of having no green balls in the first urn