Question

Here is data on the flow of students through school. 709 of freshmen pass and become sophomores, 209 fail and repeat as freshmen; 0% drop out. 809 of sophomores pass and become juniors, 10% fail and repeat as sophomores, 10% drop out. 809 of juniors pass and become seniors, 10% fail and repeat as juniors, 109 drop out. 83% of seniors pass and graduate, 790 fail and repeat as seniors, 10% drop out. Treat this as a 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 decimal places): 1. What fraction of freshmen graduate within 4 years? 2. What fraction of freshmen eventually graduate? 3. What fraction of juniors eventually graduate? 4. 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? (in years)

Name: here is data on the flow of students through school 709 of freshmen pass and become sophomores 209 fail and repeat as freshmen 0 drop out 809 of sophomores pass and become juniors 10 fail a 61987
Uploaded: 2023-05-15T00:36:25-08:00
Duration: 2 min 11 s
Channel: Numerade
Description: here is data on the flow of students through school 709 of freshmen pass and become sophomores 209 fail and repeat as freshmen 0 drop out 809 of sophomores pass and become juniors 10 fail a 61987

          Here is data on the flow of students through school. 709 of freshmen pass and become sophomores, 209 fail and repeat as freshmen; 0% drop out. 809 of sophomores pass and become juniors, 10% fail and repeat as sophomores, 10% drop out. 809 of juniors pass and become seniors, 10% fail and repeat as juniors, 109 drop out. 83% of seniors pass and graduate, 790 fail and repeat as seniors, 10% drop out. Treat this as a 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 decimal places): 
1. What fraction of freshmen graduate within 4 years?
2. What fraction of freshmen eventually graduate?
3. What fraction of juniors eventually graduate?
4. 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? (in years)

Added by Antonio H.

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