Question

Each American family is classified as living in an urban, rural, or suburban location. During a given year, 4% of all urban families move to a suburban location, and 15% move to a rural location; also, 5% of all suburban families move to an urban location, and 4% move to a rural location; finally 6% of all rural families move to an urban location, and 6% move to a suburban location. (a) If a family now lives in an urban location, what is the probability that it wil live in an urban area two years from now? A suburban area? A rural area? (b) Suppose that at present, 25% of all families live in an urban area, 40% live in a suburban area, and 35% live in a rural area. Three years from now, what percentage of American families will live in an urban area? (c) What problems might occur if this model were used to predict the future population distribution of the United States?

Answer 1

I have given a detailed explanation.Hope that helps.

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continued..

As we can see above, probabilities keep changing year on year. Likewise, when people's preferences change according to the current trends, the probability of the actual movement of families will also change.Thus making it a non -stationary Markov chain.