Consider a Markov Chain with the following state diagram. 0.2 A B 0.4 0.2 0.1 0.2 0.4 C 1) Find the transition matrix for this Markov Chain. ii) If the system is observed in state C, what is the probability that it is again in state C three moves later? (Note that are nine different paths that it could take for this.) iii) Find the equilibrium distribution for this system