(a) A Markov chain is described by the following transition matrix: 01 (:D 0 0 7272 Draw a graph to represent the possible chain transitions. (b) If the Markov chain starts in the first state, use the transition matrix to determine the probability of being in the third state after three steps. Use the graph to explain why this is the expected answer. (c) Use eigenvalue analysis to calculate the n step probability distribution p(). Use this (or other methods) to show that the long term distribution is {(1,1,1). (d) State, with brief reasons, what the classifications for the three states are.

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