At any given time, a subatomic particle can be in one of two states, and it moves randomly fro state to another when it is excited. If it is in state 1 on one observation, then it is 3 times as like be in state 1 as state 2 on the next observation. Likewise, if it is in the state 2 on one observati then it is 3 as likely to be in the state 2 as state 1 on the next observation.

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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 3 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 3 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. If the particle is in state 1 on the first observation, what is the probability it is in state 1 on
the fourth observation?
3. If the particle is 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?
4. If the particle is in state 1 on the fourth observation, what is the probability that it will be in
state 2 on the sixth observation and state 1 on the seventh observation?
Transcribed Image Text: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 3 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 3 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. If the particle is in state 1 on the first observation, what is the probability it is in state 1 on the fourth observation? 3. If the particle is 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? 4. If the particle is in state 1 on the fourth observation, what is the probability that it will be in state 2 on the sixth observation and state 1 on the seventh observation?
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