Within a Large Metropolitan Area, 20% of the Commuters Currently

question 130

Essay

Within a large metropolitan area, 20% of the commuters currently use the public transportation system, whereas the remaining 80% commute via automobile. The city has recently revitalized and expanded its public transportation system. It is expected that 6 months from now 30% of those who are now commuting to work via automobile will switch to public transportation, and 70% will continue to commute via automobile. At the same time, it is expected that 20% of those now using public transportation will commute via automobile and 80% will continue to use public transportation.
Let denote the state "use the public transportation system" and denote the state "commute via automobile".
Construct the transition matrix for the Markov chain that describes the change in the mode of transportation used by these commuters. Find the initial distribution vector for this Markov chain. What percentage of the commuters are expected to use public transportation 6 months from now?
__________ %

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Definitions:

Unconsummated Transaction

A business deal or trade that has been negotiated but not finalized or completed.

Tax

A compulsory financial charge or some other type of levy imposed upon a taxpayer by a governmental organization in order to fund government spending and various public expenditures.

Capitalism

An economic system characterized by private ownership of the means of production, competition, and the pursuit of profit.

Self-Interest

Self-interest is a concept in economics that denotes individuals acting in pursuit of their own benefits, often driving economic transactions and market allocations.