Assume that a student going to a certain four-year medical school in northern New England has, each year, a probability q of flunking out, a probability r of having to repeat the year, and a probability p of moving on to the next year (in the fourth year, moving on means graduating).
(a) Form a transition matrix for this process taking as states F, 1, 2, 3, 4, and G where F stands for flunking out and G for graduating, and the other states represent the year of study.
(b) For the case q = .1, r = .2, and p = .7 find the time a beginning student can expect to be in the second year. How long should this student expect to be in medical school?
(c) Find the probability that this beginning student will graduate.