A simulation of random walks for use as an educational device.

Abstract

The usefulness of random walks in mathematical modeling is often overshadowed by the problems that confront both students and instructors of probability. The counter-intuitive conclusions which arise produce both ambiguities and misunderstandings. In this thesis, the techniques of computer simulation have been combined with the visual appeal of interactive graphic displays to develop a simulation of random walks. This simulation features interactive routines which are easy to use and take advantage of the insight and visual capabilities of the user to build an intuitive background of the subject matter. Statistics whose empirical distributions are asymptotically Arc Sine and Normal plus the gambler's ruin problem are displayed under various experimental conditions which the user designs. This simulation is appropriate for use both by instructors to complement their classroom presentations and by students to enhance their understanding of the theory.