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Give two interpretation of what the first entry of the distribution (the limiting distribution of the markov chain) tells you based on the definition of a limiting distribution. Your answer should be written for a non-mathematician and should consist of between 1 and 3 complete sentences without mathematical symbols or terminology. Both interpretations should be written in this way.

Give two interpretation of what the first entry of the distribution (the limiting distribution of the markov chain) tells you based on the definition of a limiting distribution. Your answer should be written for a non-mathematician and should consist of between 1 and 3 complete sentences without mathematical symbols or terminology. Both interpretations should be written in this way.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 9EQ
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Give two interpretation of what the first entry of the distribution (the limiting distribution of the markov chain) tells you based on the definition of a limiting distribution. Your answer should be written for a non-mathematician and should consist of between 1 and 3 complete sentences without mathematical symbols or terminology. Both interpretations should be written in this way.

Let X₁, X₁,... be the Markov chain on state space {1,2,3,4} with transition matrix 1/2 1/2 0 1/7 0 0 0 0 3/7 3/7 1/3 1/3 1/3 2/3 1/6 1/6/ (b) Find the limiting distribution for this Markov chain. For the final two parts of this question, assume that this Markov chain is a model¹ of a country's economy. State 1 represents being 'in recession' and other states represent other broad categories of behaviour such as 'growing slowly'. The X; (for i E N) represent the state the economy is in during the ith month after we started observing it. (d) Give an interpretation of what the first entry of the distribution you found in part (b) tells you based on the definition of a limiting distribution. Your answer should be written for a non-mathematician and should consist of between 1 and 3 complete sentences without mathematical symbols or terminology. Give one other interpretation of the first entry of the distribution you found in part (b) written in the same style as for part (d).
Transcribed Image Text:Let X₁, X₁,... be the Markov chain on state space {1,2,3,4} with transition matrix 1/2 1/2 0 1/7 0 0 0 0 3/7 3/7 1/3 1/3 1/3 2/3 1/6 1/6/ (b) Find the limiting distribution for this Markov chain. For the final two parts of this question, assume that this Markov chain is a model¹ of a country's economy. State 1 represents being 'in recession' and other states represent other broad categories of behaviour such as 'growing slowly'. The X; (for i E N) represent the state the economy is in during the ith month after we started observing it. (d) Give an interpretation of what the first entry of the distribution you found in part (b) tells you based on the definition of a limiting distribution. Your answer should be written for a non-mathematician and should consist of between 1 and 3 complete sentences without mathematical symbols or terminology. Give one other interpretation of the first entry of the distribution you found in part (b) written in the same style as for part (d).
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