Using Stochastic Matrices to Predict Population Move- ment The objective of this project is to try to predict the population of people living in cities, suburbs, and non-metropolitan (rural) areas based off of the number of people living in cities, suburbs, and rural areas in 1995. You may wish to consult the Statistical Abstract of the United States for that year. Next, determine the following probabilities for 1995 1. The probability of a person staying in the city. 2. The probability of a person leaving the city and moving to the suburbs. 3. The probability of a person leaving the city and moving to a rural area. 4. The probability of a person leaving the suburbs for the city. 5. The probability of a person remaining in the suburbs. 6. The probability of a person leaving the suburbs for a rural area. 7. The probability of a person leaving a rural area for the city. 8. The probability of a person leaving a rural area for the suburbs 9. The probability of a person remaining in a rural area. Define X as: [ City Population in 1995 Xo = Suburb Population in 1995 Rural Population in 1995 Then the population n years from 1995, X, can be found by computing X. p. X. Where P represent the 3 x 3 Stochastic matrix created using the above prob abilities as the entries of the rows. Write a small program in C++ or MAT- LAB) to try to predict the number of people living in cities, suburbs, and non- metropolitan areas in 2005 and 2015. Then compare your finds with the exact number of people living in those areas during those years by again consulting the Statistical Abstract of the United States for those years. Find the relative error between your calculated solution and the exact solution. Then summarize your findings in a report. Make sure that you turn in your program and your report when you come to take your final exam. Show transcribed image text Using Stochastic Matrices to Predict Population Move- ment The objective of this project is to try to predict the population of people living in cities, suburbs, and non-metropolitan (rural) areas based off of the number of people living in cities, suburbs, and rural areas in 1995. You may wish to consult the Statistical Abstract of the United States for that year. Next, determine the following probabilities for 1995 1. The probability of a person staying in the city. 2. The probability of a person leaving the city and moving to the suburbs. 3. The probability of a person leaving the city and moving to a rural area. 4. The probability of a person leaving the suburbs for the city. 5. The probability of a person remaining in the suburbs. 6. The probability of a person leaving the suburbs for a rural area. 7. The probability of a person leaving a rural area for the city. 8. The probability of a person leaving a rural area for the suburbs 9. The probability of a person remaining in a rural area. Define X as: [ City Population in 1995 Xo = Suburb Population in 1995 Rural Population in 1995 Then the population n years from 1995, X, can be found by computing X. p. X. Where P represent the 3 x 3 Stochastic matrix created using the above prob abilities as the entries of the rows. Write a small program in C++ or MAT- LAB) to try to predict the number of people living in cities, suburbs, and non- metropolitan areas in 2005 and 2015. Then compare your finds with the exact number of people living in those areas during those years by again consulting the Statistical Abstract of the United States for those years. Find the relative error between your calculated solution and the exact solution. Then summarize your findings in a report. Make sure that you turn in your program and your report when you come to take your final exam.

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Answer to Using Stochastic Matrices to Predict Population Move- ment The objective of this project is to try to predict the popula…