[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Assume that a student going to a certain four-year medical school in northern New England has, each year, a probability [math]q[/math] of flunking out, a probability [math]r[/math] of having to repeat the year, and a probability [math]p[/math] of moving on to the next year (in the fourth year, moving on means graduating).

• 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.
• For the case [math]q = .1[/math], [math]r = .2[/math], and [math]p = .7[/math] 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?
• Find the probability that this beginning student will graduate.