The Registrar of a Law School Has Compiled the Following

question 109

Essay

The registrar of a law school has compiled the following statistics on the progress of the school's students working toward the LLB degree: Of the first-year students in a particular year, 85% successfully complete their course of studies and move on to the second year, whereas 15% drop out of the program; of the second-year students in a particular year, 92% go on to the third year, whereas 8% drop out of the program; of the third-year students in a particular year, 98% go on to graduate at the end of the year, whereas 2% drop out of the program.
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Construct the transition matrix associated with the Markov process.
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Please round the answers to the nearest thousandth, if necessary.
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Find the steady-state matrix.
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Determine the probability that a beginning law student enrolled in the program will go on to graduate.

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Definitions:

Aggregate Supply

The total supply of goods and services that firms in an economy plan on selling during a specific time period.

Government Intervention

The direct or indirect involvement of governmental actions in the market to influence the economy, correct market failures, or protect the public interest.

John Maynard Keynes

A British economist whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments, emphasizing the importance of government intervention during economic downturns.

Milton Friedman

An influential American economist known for his strong belief in free-market capitalism and for winning the Nobel Prize in Economic Sciences in 1976.