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2. (20 pts) Consider a MC given by the state-transition diagram below: 1/2 O 1 2 1/3 1/2 1/3 1/3 (a) (5 pts) Find the

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2. (20 pts) Consider a MC given by the state-transition diagram below: 1/2 O 1 2 1/3 1/2 1/3 1/3 (a) (5 pts) Find the probability that the process, starting in state 0, will be in state 2 at time 4. (b) (15 pts) Find the probability that n = 9 will be the first time that the process, starting in state 0, will return to state 0

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