Let the process of getting through undergraduate school be a homogeneous Markov process with time unit one year. The states are Freshman, Sophomore, Junior, Senior, Graduated, and Dropout. Your class (Freshman through Graduated) can only stay the same or increase by one step, but you can drop out at any time before graduation. You cannot drop back in. The probability of a Freshman being promoted in a given year is .8; of a Sophomore, .85; of a Junior, .9, and of a Senior graduating is .95. The probability of a freshman dropping out is .10; of a Sophomore, .07; of a Junior, .04; of a Senior, .02. a) Construct the Markov transition matrix for this process.
b) If we were more realistic, and allowed for students dropping back in, this would no longer be a Markov process. Why not?