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On Any Particular Day,an Individual Can Take One of Two

question 21

Essay

On any particular day,an individual can take one of two routes to work.Route A has a 25% chance of being congested,whereas route B has a 40% chance of being congested.The probability of the individual taking a particular route depends on his previous day's experience.If one day he takes route A and it is not congested,he will take route A again the next day with probability 0.8.If it is congested,he will take route B the next day with probability 0.7.On the other hand,if he takes route B one day and it is not congested,he will take route B again the next day with probability 0.9.Similarly,if route B is congested,he will take route A the next day with probability 0.6.
a.Construct the transition matrix for this problem.(Hint: There are four states corresponding to the route taken and the congestion.The transition probabilities are products of the independent probabilities of congestion and next-day choice.)
b.What is the long-run proportion of time that route A is taken?

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Definitions:

Obscene Material

Content considered offensive or inappropriate by the standards of public decency and morality, often sexual in nature, and regulated by law in many jurisdictions.

Political Environment

The context created by political institutions, processes, and activities that influence the operation of societies and businesses.

Fair Trade Commission

The Fair Trade Commission is a government agency responsible for promoting fair business practices and competition by enforcing laws related to antitrust and consumer protection.

U.S. Interstate

A network of controlled-access highways that form part of the National Highway System in the United States.