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. Researchers estimate that the particle is currently times as like to be in state 1 as state 2. Find the probability vector representing this estimation. 3. Based on this estimation, what is the probability that the particle will be in state 2 two weeks from now? 4. What is the probability that the particle will be in the state 1 three weeks from now?
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. Researchers estimate that the particle is currently times as like to be in state 1 as state 2. Find the probability vector representing this estimation. 3. Based on this estimation, what is the probability that the particle will be in state 2 two weeks from now? 4. What is the probability that the particle will be in the state 1 three weeks from now?
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.4: Hyperbolas
Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
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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. Researchers estimate that the particle is currently 5 times as like to be in state 1 as state 2. Find the probability vector representing this estimation.
3. Based on this estimation, what is the probability that the particle will be in state 2 two weeks from now?
4. What is the probability that the particle will be in the state 1 three weeks from now?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffde8eb56-498e-4c1b-bbe7-9b5745d748fc%2Fd7895b04-f7a4-4396-8f5a-320f209b7eab%2F1pzq82g_processed.jpeg&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. Researchers estimate that the particle is currently 5 times as like to be in state 1 as state 2. Find the probability vector representing this estimation.
3. Based on this estimation, what is the probability that the particle will be in state 2 two weeks from now?
4. What is the probability that the particle will be in the state 1 three weeks from now?
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