Suppose a two-state experiment has the following transition matrix: 1 P = 0.5 0.5 Answer the following questions: 1. If the experiment is in state 1 on the first observation, what is the probability it will be in state 2 on the second observation? 2. If the experiment is in state 1 on the first observation, what is the probability it will be in state 2 on the fourth observation? 3. If the experiment is in state 2 on the third observation, what is the probability that it will be in state 2 on the seventh observation?

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 31E
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Suppose a two-state experiment has the following transition matrix:
1
P
0.5
0.5
Answer the following questions:
1. If the experiment is in state 1 on the first observation, what is the probability it will be in state 2 on the
second observation?
2. If the experiment is in state 1 on the first observation, what is the probability it will be in state 2 on the
fourth observation?
3. If the experiment is in state 2 on the third observation, what is the probability that it will be in state 2 on
the seventh observation?
4. If the experiment is in state 1 on the third observation, what is the probability it will be in state 1 on the
fourth, fifth, and sixth observation?
Transcribed Image Text:Suppose a two-state experiment has the following transition matrix: 1 P 0.5 0.5 Answer the following questions: 1. If the experiment is in state 1 on the first observation, what is the probability it will be in state 2 on the second observation? 2. If the experiment is in state 1 on the first observation, what is the probability it will be in state 2 on the fourth observation? 3. If the experiment is in state 2 on the third observation, what is the probability that it will be in state 2 on the seventh observation? 4. If the experiment is in state 1 on the third observation, what is the probability it will be in state 1 on the fourth, fifth, and sixth observation?
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