. 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 of having to repeat the year and probability r of passing [p -\- q-\-r= 1). The states are:

dropped out (s,), graduated (5 2 ), 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.)