For the Markov chain of Exercise , find the average number of years a first-year, second-year and third-year student will remain in university.
Exercise
The following problem is based upon one in Kemeny and Snell (1960). In each year of a three -year degree course, a university student has probability p of not returning the following year, probability q ofhaving to repeat the year and probability r of passing (p +q +r = 1).
The states are: dropped out (s1); graduated (S2), is a third-year student (S3), is a secondyear student (S4); and is a first-year student (S5); Find the transition matrix P and the matrices Q and R.
(Note that this is a random walk with absorbing barriers.)