The apps in this project are designed to demonstrate the mathematical theory in a dynamic, interactive way. Each app runs in a separate window, with the small amount of text necessary to describe the app and its notation, but with little explicit mathematical exposition. Thus, the apps can be used with the expository portion of this project, or by themselves, at various mathematical levels.

The apps generally fall into two basic types:

• Simulation apps. These are simulations of random processes, designed to show the agreement between the predictions of the mathematical theory and the behavior of the process. These are generally referred to as experiments in the text. Generally, the student can vary parameters and choose among various probability distributions that drive the simulation.
• Data generation apps. These are apps in which the student generates the data, by making choices in a game, or clicking in a scatterplot or number line. These are generally referred to as games in the text.

Browser Requirements

The apps are based on a number of open and standard technologies, including HTML5, CSS, SVG, and JavaScript. To use this project properly, you will need a web browser that supports these technologies. The latest versions of most modern browsers should work well. Display of mathematical notation is handled by the open source MathJax project.

Graphical User Interface

A standard Graphical User Interface (GUI) is used, with command buttons, scrollbars and list boxes. There is no programming or command language, so students should be able to run the apps with little or no instructions. The apps run in a separate window, so that the student can easily move back and forth between the apps and the corresponding hypertext discussion, and so that a student can keep an app open and running as she browses through the text.

The app output is displayed numerically and graphically in a set of coordinated tables and graphs. A consistent color-coding is used. Graphical objects that depend only on the distributions or parameters are usually shown in blue, while graphical objects that depend on data (either simulation or student generated) are usually shown in red. Most app objects have tool tips, small pop-up boxes that explain the object. Rest the cursor on an object to display the tool tip.

The Main Toolbar

Apps that are simulations of random processes all have the Main Toolbar with the following basic buttons and contorts:

• Step. This button runs the experiment one time, updating data and graphs. In some cases sound and delays are incorporated to give the student maximum feedback about the random process.
• Run. This button runs the experiment repeatedly. The frequency of data and graphical updates can be controlled by the student. No sounds or delays are incorporated so that the simulation will run fast.
• Stop. This button stops the simulation but preserves all data and graphs.
• Reset. This button clears all simulation data and graphs and restores the random process to its initial state.

The stop frequency is selected from the second list box in the main toolbar. The stop frequency is the number of runs before the simulation stops in run mode. In most apps you can select a stop frequency of 100, 1000, or 10000. In some apps, other stop rules are provided.

Parameter Toolbars

The user can vary the parameters, select distributions, and choose among appropriate modeling assumptions using list boxes, scrollbars, and pop-up dialog boxes. These controls appear on parameter toolbars at the top of the app window, below the main toolbar.