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?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...
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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?
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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