Introduction and Background

This document discusses the use of technology support tools — primarily Mathematica and Excel, with a few notes on scientific calculators — in support of a one-semester college course in Probability and Statistics—specifically MA206, taught by the Department of Mathematical Sciences, United States Military Academy. The target audience is an instructor in the course who has a basic familiarity with Mathematica, Excel, and related tools, but wants to understand how to use the tool in support of the course. This document is not intended to be either a complete tutorial or a replacement for the course text; it is intended to assist the instructor in understanding how to work with the program in support of the course philosophy.

As the primary tool for much of the course is Mathematica, and most instructors are reasonably familiar with Excel, much of the emphasis of this document is on Mathematica manipulations.

This paper is not aimed at students in the course, although some students may find it interesting; the principle pitfall for students is that this paper discusses issues that may be a dstraction to students who should be focused on mastering the course material.

Course Philosophy

MA 206 is an introduction to probability and statistics, and is part of the core curriculum at USMA.  As such, it is a required course for all cadets, regardless of major, and is normally taken in the spring of the second year, after successful completion of  courses in mathematical modeling, differential calculus, and integral calculus.

The underlying approach to the course is to define the cumulative distribution function as a model fitted to the data — tabulated in the form of an empirical distribution function — and then to extend the manipulations of this model into calculations of probability and finally traditional statistical methods such as confidence intervals and hypothesis tests.

Throughout the development of the material, the connection of the material to methods learned in previous courses is emphasized. For example, instead of deriving formulæ for the expected value of each distribution encountered, cadets are expected to calculate the expected value directly from the definition, as a definite integral — a task made markedly easier by the routine use of Mathematica.

Topics are presented in an order intended to support this approach to the subject. In many cases, the material is presented in two ways. The primary approach exploits the standard Mathematica functions that express concepts cadets have learned in prior courses; this reinforces the earlier concepts and provides a bridge to the probability and statistics related concepts of this course.  An alternate approach is sometimes shown, primarily for the benefit of instructors, that uses more advanced Mathematica functionality for the same purpose.

Created by Mathematica  (July 20, 2006)