Concept explainers
Housing Patterns In a survey investigating changes in housing patterns in one urban area, it was found that 75% of the population lived in single-family dwellings and 25% in multiple housing of some kind. Five years later, in a follow-up survey, of those who had been living in single-family dwellings, 90% still did so, but 10% had moved to multiple-family dwellings. Of those in multiple-family housing, 95% were still living in that type of housing, while 5% had moved in single-family dwellings. Assume that these trends continue.
(a) Write a transition matrix for this information.
(b) Write a probability
What percent of the population can be expected in each cat- [ energy after the following time periods?
(c) 5 years (d) l0 years
(e) Write the transition matrix for a 10-year period.
(f) Use your result from part (e) to find the probability that someone living in a single-family dwelling is still doing so 10 years later.
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