A Computer Algebra System (CAS) such as MAPLE can be used to manipulate symbols. The graphical capability of a CAS can help students visualize expressions that are manipulated symbolically. A CAS can also be used to do numerical calculations. Simulation can be incorporated in a variety of applications.

For this talk we will consider the definition of the t-distribution and see what can go wrong if certain hypotheses are not satisfied.

The statistics package that comes with MAPLE is not complete. However, Zaven Karian has written more than 130 additional procedures to support instruction in probability and statistics. These procedures are available at no cost and several will be incorporated into this talk.

To get started, click on the following command line to load the supplementary statistics package as well as some other procedures that will be used.

> restart: read `e:stat.m`: with(plots): randomize(): with(student):
read `e:ProbHistFill.txt`: read `e:EmpCDF.txt`:
read `e:HistogramFill.txt`:read `e:ProbHistB.txt`:
read `e:ProbHistFillY.txt`:
read `e:ScatPlotCirc.txt`:
read `e:ScatPlotPoint.txt`: read `e:BoxPlot.txt`:

>

Discrete Distribution Example

Definition of Student's T-Distribution

When Does "T " Really Have a T-Distribution?

Volume of a ball of radius one in n-space

Sums of Discrete Random Variables

Sums of Continuous Random Variables

Limits of Moment-Generating Functions

Acknowledgements