Classical Probability Application: A Discrete Dynamical System Defined by a Markov Chain

Abstract

ADDRESS: (I)Dep artment of Mathematical Sciences, United St ates Military Academy, West Point NY 10996 USA and (2) Department of Mathem atics and St atisti cs, The College of New J ersey, Tr enton NJ 08650-4700 USA.ABSTRACT: Each st ude nt at th e Un it ed States Military Acad emy t akes a four course sequence in core mathematics. As th e final core mathematics capstone course, probability and st atistics (P&S) not only includes t he st and ard material of such a course , but also ask s the students to reflect upon previous core mathematics topics. Sinc e our probability course covers continuous un ivariate and multivariate distributions , calc ulus (core courses 2 and 3) alr eady assumes a significant role. It was our desire that the st ude nts utilize their modeling skills gain ed in the first cor e course, Discr et e Dyn amical Syst ems (DDS). This led to a P&S project that requires DDS to find the steady-s tate probabilities of a Markov Chain. These steady-state probabilities are then used in a larger Bayes ' Theorem and conditional probability scenario.