Suppose that the following data were obtained from the records of a certain two-year college: Of those who were freshmen (F) during a particular year, 80% became sophomores (S) the next year and 20% dropped out (D). Of those who were sophomores during a particular year, 90% graduated (G) by the next year and 10% dropped out.
(a) Set up the absorbing stochastic matrix with states D, G, F, S that describes this transition.
(b) Find the stable matrix.
(c) Determine the probability that an entering freshman will eventually graduate.
(d) Determine the expected number of years that a student entering as a freshman will attend the college before either dropping out or graduating?