At any given time, a subatomic particle can be in one of two states, and it moves randomly from one state to another when it is excited. If it is in state 1 on one observation, then it is 2 times as likely to be in state 1 as state 2 on the next observation. Likewise, if it is in the state 2 on one observation, then it is 2 as likely to be in the state 2 as state 1 on the next observation. 1. Find the transition matrix for this Markov chain. 2/3 1/3 1/3 2/3 2. If the particle is in state 1 on the first observation, what is the probability it is in state 1 on the fourth observation? 14/ 3. If the particle in state 2 currently, what is the probability that it will be in state 2 then state 1 then state 1 then state 2 on the next four observations? 0.0.

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