Classical probability application: A discrete dynamical system defined by a markov chain

Each student at the United States Military Academy takes a four course sequence in core mathematics. As the final core mathematics capstone course, probability and statistics (P&S) not only includes the standard material of such a course, but also asks the students to reflect upon previous core mathematics topics. Since our probability course covers continuous univariate and multivariate distributions, calculus (core courses 2 and 3) already assumes a significant role. It was our desire that the students utilize their modeling skills gained in the first core course, Discrete Dynamical Systems (DDS). This led to a P&S project that requires DDS to find the steady-state probabilities of a Markov Chain. These steady-state probabilities are then used in a larger Bayes’ Theorem and conditional probability scenario.