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PROBLEM # 2 (35 points) Consider the discrete Markov Chain represented in the following state-transition diagram: (a) (10 points) Identify the classes and states in each class, and classify the classes and states. If a state is periodic, indicate its period. (b) (10 points) Reduce the class containing state 5 to a single (aggregate) state, called state 5'. Then, compute the absorption probability from state 3 to state 5'. (c) (15 points) Using the solution of part (b), compute the long-run distribution given that the process starts in state 3