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 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 s 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. If the particle is in state 1 on the first observation, what is the probability it is in state 1 on the fourth observation?
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 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 s 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. If the particle is in state 1 on the first observation, what is the probability it is in state 1 on the fourth observation?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 47RE
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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 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. 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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36a79c17-bf73-44c3-9503-d2f30f855206%2F5e35da08-95a4-4d2c-9c60-22c6a4834748%2Fzcu92r5_processed.png&w=3840&q=75)
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 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. 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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