\chapter{Introduction}

For the past three years, the course on Probabilistic Systems Analysis at
MIT (6.041) has used an application developed by John Piscitello
[Piscitello 91] to demonstrate how to add independent random variables.
This application was written in the Courseware Development System (CDS),
which is an authoring tool designed at MIT written for Xwindows.  It was
designed to make writing lecture and educational programs extremely easy,
by providing a simple graphical interface to many powerful backends.  The
language used by CDS aplications would consist of only a few high-level
functions, to maximize the ease of programming in CDS.  [Piscitello 8]
Piscitello's application was intended for the lecturer, to give an easy
way to teach random variables and convolution.  Although this application
has been extremely useful, CDS is no longer supported and now only runs
on VAXstation 3100s.  As the VAXes are becoming obsolete, this project
was required to port the random variable application to a platform that
is still supported.  

\paragraph{}

The purpose of this project was to write a new application in a newer
supported platform to supplant Piscitello's.  The new application is
named RVadd, and is written in cT, version 2.2.  Many of the features of
Piscitello's application are incorporated into RVadd, and several new
features have been added to make the application even easier to use.  In
addition, the intended audience has been widened to allow students to
actually use the program to learn convolution. 

\section{Pedagogical Objectives}

The main pedagogical objectives of this application are to provide an
easy way for students to learn the concepts behind adding independent random
variables and how convolution works.  RVadd must be able to demonstrate
several separate concepts.

\begin{enumerate}

\item What does it mean to ``add'' two independent random variables?

\item How are calculations performed using sample space?

\item How convolution provides an algorithm that keeps track of the
necessary accounting and simplifies the calculations.

\item What are the effects of convolving two independent random variables?

\begin{itemize}

\item The minimum of the sum of two independent random variables is the sum of the minimum
values.

\item The maximum of the sum of two independent random variables is the sum of the maximum
values.

\item The expected value of the sum of two independent random variables is the sum of the
two expected values.

\item The expected variance of the sum of two independent random variables is the sum
of the two expected variances.

\end{itemize}
\end{enumerate}

%%\paragraph{}
%%
%%\begin{itemize}
%%
%%\item theory of convolution
%%\item pedagogical objectives
%%\item what does it mean to add RV?
%%\item samplespace
%%\item how does convolution work
%%\item general effects of adding RV's
%%\item use of transforms --- ?????
%%\item continuous RV's
%%
%%\end{itemize}
%%
%%\paragraph{}
%%
%%This document is written primarily for future students with similar
%%projects, either upgrading RVadd or designing other cT applications.
%%Hopefully, it will be able to assist in improved designs in the future.


