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Lab Experiments in Probability

James A. Reising

University of Evansville

Abstract

The subject of probability occurs not only in courses on probability and statistics, but also in courses covering stochastic processes. The concept of using probability models to describe real- life problems seems difficult for many students to grasp. Mathematical software, such as MATLAB, provides a useful tool in performing simulations using probability models.

To assist students in forming a conceptual link between the results of actual experiments and practical situations in which the outcome is predictable only in a probabilistic sense, several simple projects involving repeated trials of an experiment are used in a course in probability or random signals. MATLAB programs simulating the same experiment are assigned as part of each project.

This paper describes several such experiments and the associated MATLAB simulations. Students working in groups of three or four compare their experimental results with the MATLAB simulations and to the results of other groups in the class.

By comparing the actual and simulated results, students may develop some confidence in the use of computational software to simulate experiments for larger numbers of trials than they can realistically perform in practice.

Introduction

Random variables are a key concept in the study of probability and random processes. The expected value and variance of a random variable are key concepts in probability theory1. These definitions can be extended to sums of random variables2. Let X i represent one of a number of discrete random variables and E[ X i ] the expected value of X i . For a sum of n random variables,

E[∑i =1 X i ] = ∑i =1 E[ X i ] n n (1)

is generally true2. If the X i are mutually independent,

Var[∑i =1 X i ] = ∑i =1Var[ X i ] n n (2)

"Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright © 2005, American Society for Engineering Education"

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Reising, J. (2005, June), Lab Experiments In Probability Paper presented at 2005 Annual Conference, Portland, Oregon. 10.18260/1-2--15390