Here is data on the flow of students through a school. 70% of freshmen pass and become sophomores, 20% fail and repeat as freshmen, 10% drop out 80% of sophomores pass and become juniors, 10% fail and repeat as sophomores, 10% drop out 80% of juniors pass and become seniors, 10% fail and repeat as juniors, 10% drop out 82% of seniors pass and graduate, 8% fail and repeat as seniors, 10% drop out Treat this as a 6-state Markov chain with "graduated" and "dropped out" being absorbing states. Use an appropriate matrix tool to answer the following questions. (Give your answers correct to 3 decimal places.) (a) What fraction of freshmen graduate within 4 years? (b) What fraction of freshmen graduate within 5 years? (c) What fraction of freshmen eventually graduate?
Here is data on the flow of students through a school. 70% of freshmen pass and become sophomores, 20% fail and repeat as freshmen, 10% drop out 80% of sophomores pass and become juniors, 10% fail and repeat as sophomores, 10% drop out 80% of juniors pass and become seniors, 10% fail and repeat as juniors, 10% drop out 82% of seniors pass and graduate, 8% fail and repeat as seniors, 10% drop out Treat this as a 6-state Markov chain with "graduated" and "dropped out" being absorbing states. Use an appropriate matrix tool to answer the following questions. (Give your answers correct to 3 decimal places.) (a) What fraction of freshmen graduate within 4 years? (b) What fraction of freshmen graduate within 5 years? (c) What fraction of freshmen eventually graduate?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Here is data on the flow of students through a school.
70% of freshmen pass and become sophomores, 20% fail and repeat as freshmen, 10% drop out
80% of sophomores pass and become juniors, 10% fail and repeat as sophomores, 10% drop out
80% of juniors pass and become seniors, 10% fail and repeat as juniors, 10% drop out
82% of seniors pass and graduate, 8% fail and repeat as seniors, 10% drop out
80% of sophomores pass and become juniors, 10% fail and repeat as sophomores, 10% drop out
80% of juniors pass and become seniors, 10% fail and repeat as juniors, 10% drop out
82% of seniors pass and graduate, 8% fail and repeat as seniors, 10% drop out
Treat this as a 6-state Markov chain with "graduated" and "dropped out" being absorbing states. Use an appropriate matrix tool to answer the following questions. (Give your answers correct to 3 decimal places.)
(a) What fraction of freshmen graduate within 4 years?
(b) What fraction of freshmen graduate within 5 years?
(c) What fraction of freshmen eventually graduate?
(d) What fraction of juniors eventually graduate?
(e) Assume that a student enters the school as a senior. What is the expected value for the number of years that person will spend in school before either graduating or dropping out?
years
(b) What fraction of freshmen graduate within 5 years?
(c) What fraction of freshmen eventually graduate?
(d) What fraction of juniors eventually graduate?
(e) Assume that a student enters the school as a senior. What is the expected value for the number of years that person will spend in school before either graduating or dropping out?
years
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