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Mathcad™ for In-class Examples in a Random Processes Course Abstract

Some textbooks1,2 used for courses in Probability and Random Processes use MATLAB™ for computer demonstrations and exercises, while others3,4,5 do not emphasize specific computer exercises or examples, and at least one6 uses C programs. I find it convenient to use Mathcad for lecture examples. The appearance of calculations onscreen is practically identical to equations appearing in the text, and graphs of illustrative results appear on the same page as the equations. Calculations are all "live", causing graphs to be updated when the values of one or more parameters are changed. This rapid response provides faster visual representation of important concepts.

This paper gives examples of Mathcad worksheets for use during lecture in a course discussing probability and random processes. The ability to easily and quickly change parameters used in the equations with automatic updating of graphical display of results helps illustrate the concepts involved.

Background

EE 413 Random Signals and Noise has been offered three times at the University of Evansville. By the second offering it had become obvious that students found many of the concepts in probability and random processes difficult to grasp, and the need for additional in-class examples was apparent. I used Mathcad examples in class for the first time in the fall semester 2005.

The textbooks1,2 used (in different semesters) both use MATLAB in sample problems and homework. MATLAB is used as well in a number of other courses in the EE curriculum and is available on the department network, so students need not purchase the program. I have found it useful to use Mathcad during lecture for illustrating the role of various parameters in probabilistic examples for the reasons cited in the abstract section above. I use Mathcad only for lecture examples, so students need not use or purchase the software.

Probability Density and Distribution Functions

The probability density function of a random variable X, f X (x) , and the cumulative probability distribution function of X, FX (x) , are key concepts in the study of random variables. Mathcad includes built-in functions for common distributions of both discrete and continuous random variables, including the discrete binomial and Poisson distributions, and the continuous exponential, Cauchy, and Gaussian (normal) distributions. All these functions include one or more parameters characterizing a particular instance of the distribution. Simple plots of the density and distributions functions can be used in class to examine the effects of varying the values of the parameters.

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Reising, J. (2006, June), Mathcad For In Class Examples In A Random Processes Course Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. 10.18260/1-2--460