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 out80% of sophomores pass and become juniors, 10% fail and repeat as sophomores, 10% drop out80% of juniors pass and become seniors, 10% fail and repeat as juniors, 10% drop out82% of seniors pass and graduate, 8% fail and repeat as seniors, 10% drop outTreat 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?