1† The State College admissions office has modeled the path of a student through State College as a Markov chain:

Each student’s state is observed at the beginning of each fall semester. For example, if a student is a junior at the beginning of the current fall semester, there is an 80% chance that he will be a senior at the beginning of the next fall semester, a 15%
chance that he will still be a junior, and a 5% chance that he will have quit. (We assume that once a student quits, he never reenrolls.)
a If a student enters State College as a freshman, how many years can he expect to spend as a student at State?
b What is the probability that a freshman graduates?

Transcribed Image Text:

F So. J. Sen. Q. G. Freshman .10 .80 00 .10 0 Sophmore 0 .10 .85 0 .05 0 Junior 0 0 .15 .80 .05 0 Senior 0 0 0 .10 .05 .85 Quits 0 0 0 0 1 Graduates 0 0 0 0 0 10