The goal of this project is to provide a set of free, high quality, web-based resources for students and teachers of probability and statistics. Many of the elements are designed so that they can be modified and reused to fit the needs of students at various levels. The project has two basic types of resources:
All ancillary materials open in small pop-up windows. Thus, these materials can remain open and accessible while you browse the expository material in the main window. The expository material has extensive links to the ancillary materials, but some of these materials are also designed to stand alone so that they can be used in other projects. The ancillary materials are of the following types:
The major components of the project are discussed in more detail below.
This project uses HTML5 web technologies. Almost all of these tecnologies are open, published standards endorsed by various standards groups, including the World Wide Web Consortium. One of our goals is for this site to be fully standards-compliant and to implement best practices for web-based expository mathematics. The list below describes the main technologies used; follow the links for more information.
Mathematical expressions rendered by MathJax scale appropriately with the surrounding text, and can be copied and pasted into other applications.
The expository material is divided into chapters, similar to chapters in a conventional book. The chapters explore the basic theory and applications of probability, statistics, and certain special models and random processes. Each chapter in turn is divided into web
pages, similar to sections in a conventional book. Each section explores a particular topic, mostly through a series of exercises that guide the student through the development of the mathematical theory and the development of probabilistic intuition.
The expository text assumes knowledge of calculus, at the standard undergraduate level. A few sections require knowledge of linear algebra, at the standard undergraduate level. No prior knowledge of probability or statistics is assumed. A few sections contain advanced ideas involving measure theory or analysis, but these sections are identified and can be omitted if necessary.
As we have already noted, the expository material is mostly in the form of exercises. These are of three basic types, each keyed with a special icon.
Proofs of most theoretical exercises and answers for most computational exercises are provided. On supported browsers (Chrome, Safari and other WebKit browsers), you can expand and contract the proofs and answers. At the top of each expository page (in the navigation line, on the right), two buttons are provided that allow you to expand or contract all details (proofs and answers) on that page. (On other browsers, the details are always expanded, and these buttons have no effect.)
The applets are designed to demonstrate the mathematical theory in a dynamic, interactive way. Each applet runs in a separate window, with the small amount of text necessary to describe the applet and its notation, but with little explicit mathematical exposition. Thus, the applets can be used with the expository portion of this project, or by themselves, at various mathematical levels.
The applets generally fall into two basic types:
A standard Graphical User Interface (GUI) is used, with command buttons, scroll bars and list boxes. There is no programming or command language, so students should be able to run the applets with little or no instructions. The applets run in a separate window, so that the student can easily move back and forth between the applets and the corresponding exposition, and so that a student can keep an applet open and running as she browses through the text.
The applet 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 shown in blue, while graphical objects that depend on data (either simulation or student generated) are shown in red. Most applet objects have tool tips, small pop-up boxes that explain the object. Rest the cursor on an object to display the tool tip.
Applets that are simulations of random processes all have the Main Toolbar with the following basic buttons and controls:
The stop frequency is selected from the second list box on the main toolbar. The stop frequency is the number of runs before the simulation stops in run mode. In most applets you can select a stop frequency of 10, 100, 1000, or 10000. In some applets, other stop rules are provided.
The student can easily vary the parameters, select distributions, and choose among appropriate modeling assumptions using list boxes, scroll bars, and pop-up dialog boxes. These controls appear on parameter toolbars at the top of the applet window, below the main toolbar.
Our project has a number of data sets from real statistical studies, many of them historically interesting. The page for each data set has a brief description of the data set and its source. The data set itself is given either in a table or in a scrollable text area, so that the data can be copied and pasted into a statistical or spreadsheet program.. Also, in most cases, links to the data set in standard tab-separated text format and comma-separated text format are provided, so that the data set can be downloaded and opened in a statistical or spreadsheet program.
A brief biographical sketch is provided for each famous person referenced in the expository material. There are approximately 100 biographical sketches in total.
objects that make up this project are designed, to the extent possible, so that they can be re-used in other projects and modified, if necessary. The Object Library contains descriptions of of these objects and instructions for using them.
you are here navigational map is given on each page. The contents page of a chapter has links the virtual laboratories home page and to the contents pages of the other chapters. Each section in a chapter has links to the home page, to the contents page of the chapter and to the other sections in the chapter. Links that open in the main browser window are colored blue.
Additionally, the footer on each page has links to the ancillary materials that open in separate, small windows without menus or toolbars. Links to ancillary materials are colored red. Each footer also has links to the following:
Our site has links to a number of related sites in probability and statistics; these links are colored dark blue. Pages from external sites are opened in a new browser tab.