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?
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.6: Permutations And Combinations
Problem 2SC: How many different signals can be sent, when three flags are used, if two of the 9 flags are...
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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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