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Populations shifts in a certain city follow a particular pattern every year. If a person is living in the city they will stay in the city 0% of the time, move to the suburbs 50% of the time, and move out-of-state 50% of the time. If a person is living in the suburbs, they will move into the city 20% of the time, stay in the suburbs 30% of the time, and move out-of-state 50% of the time. If the person lives out-of-state, they will move to the city 10% of the time, move to the suburbs 80% of the time, and stay out-of state 10% of the time. Answer the following questions: 1. Find the transition matrix for these shifts. 2. Find the probability that an individual who is living in the city currently is living in the city two years from now. 3. What is the probability a person living in the city will remain in the city for three subsequent years? 4. What is the probability that a person living out-of-state will be either living in the city or living in the suburbs two years from now?

Populations shifts in a certain city follow a particular pattern every year. If a person is living in the city they will stay in the city 0% of the time, move to the suburbs 50% of the time, and move out-of-state 50% of the time. If a person is living in the suburbs, they will move into the city 20% of the time, stay in the suburbs 30% of the time, and move out-of-state 50% of the time. If the person lives out-of-state, they will move to the city 10% of the time, move to the suburbs 80% of the time, and stay out-of state 10% of the time. Answer the following questions: 1. Find the transition matrix for these shifts. 2. Find the probability that an individual who is living in the city currently is living in the city two years from now. 3. What is the probability a person living in the city will remain in the city for three subsequent years? 4. What is the probability that a person living out-of-state will be either living in the city or living in the suburbs two years from now?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Populations shifts in a certain city follow a particular pattern every year. If a person is living in the city they will stay in the city 0% of the time, move to the suburbs 50% of the time, and move out-of-state 50% of the time. If a person is living in the suburbs, they will move into the city 20% of the time, stay in the suburbs 30% of the time, and move out-of-state 50% of the time. If the person lives out-of-state, they will move to the city 10% of the time, move to the suburbs 80% of the time, and stay out-of state 10% of the time. Answer the following questions: 1. Find the transition matrix for these shifts. ... ... ... ... 2. Find the probability that an individual who is living in the city currently is living in the city two years from now. 3. What is the probability a person living in the city will remain in the city for three subsequent years? 4. What is the probability that a person living out-of-state will be either living in the city or living in the suburbs two years from now? ...
Transcribed Image Text:Populations shifts in a certain city follow a particular pattern every year. If a person is living in the city they will stay in the city 0% of the time, move to the suburbs 50% of the time, and move out-of-state 50% of the time. If a person is living in the suburbs, they will move into the city 20% of the time, stay in the suburbs 30% of the time, and move out-of-state 50% of the time. If the person lives out-of-state, they will move to the city 10% of the time, move to the suburbs 80% of the time, and stay out-of state 10% of the time. Answer the following questions: 1. Find the transition matrix for these shifts. ... ... ... ... 2. Find the probability that an individual who is living in the city currently is living in the city two years from now. 3. What is the probability a person living in the city will remain in the city for three subsequent years? 4. What is the probability that a person living out-of-state will be either living in the city or living in the suburbs two years from now? ...
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