Construct a model of population flow between metropolitan and nonmetropolitan areas of a given country, given that their respective populations in 2015 were 262 million and 41 million. The probabilities are given by the following matrix. (from) (to) metro nonmetro [0.99 0.02 metro 0.01 0.98 ) nonmetro Predict the population distributions of metropolitan and nonmetropolitan areas for the years 2016 through 2020 (in millions, to four decimal places). (Let x, through x, represent the years 2016 through 2020, respectively.) 261.21 43.79 X 259.4737 45.5263 X 2657.789 X 3 47.2105 X 256.1558 XA 48.8442 X 254.5711 X5 50.4289 X If a person was living in a metropolitan area in 2015, what is the probability that the person will be living in a nonmetropolitan area in 2020? (Round your answer to four decimal places. 0.9679 1xThe following matrix gives occupational transition probabilities. (initial generation) nonfarming farming 0.3 nonfarming 0.7] (next generation) farming (a) If the father is a farmer, what is the probability that the son will not be a farmer? 0.07 X (b) If there are 14,000 in the nonfarming category and 3,000 in the farming category at a certain time, what will the distribution be one generation after the initial generation? What will the distribution be four generations after the initial generation? (c) If a man is a farmer, what is the probability that his grandson will be a farmer? 0.52