Absorbing Chain Problem (20 points)According to the University Registrar, a student’s status (freshman, sophomore, junior, or senior) depends on thenumber of credits earned. According to (made-up) historical data:?A freshman has a 5% probability of staying as a freshman the following year, a 75% probability of becoming asophomore, and a 20% probability of dropping college and never coming back (unfortunately!).?A sophomore has an 8% probability of staying as a sophomore the following year, a 77% probability ofbecoming a junior, and a 15% probability of dropping college and never coming back.?A junior has a 10% probability of staying as a junior the following year, an 80% probability of becoming asenior, and a 10% probability of dropping college and never coming back. ?Finally, a senior has a 20% probability of staying as a senior the following year (super seniors!), a 75% ofgraduating, and a 5% probability of dropping college and never coming back.a.(8 pts.)What is the expected number of years a freshman will spend in college as a freshman, a sophomore will spendin college as a sophomore, a junior will spend in college as a junior and a senior will spend in college as a senior?b.(2 pts.)According to the answer above, what is the expectedtotal number of years a new student starting next fallwill spend in college?8c.( 5pts.)What is the probability that a new student starting next fall will eventually graduate?d.( 5 pts.)What is the probability that a student who is currently a junior will eventually graduate? If any, why do you think there a discrepancy
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