Probability, Mathematical Statistics, Stochastic Processes


Basic Information

Expository Chapters

  1. Foundations
  2. Probability Spaces
  3. Distributions
  4. Expected Value
  5. Special Distributions
  6. Random Samples
  7. Point Estimation
  8. Set Estimation
  9. Hypothesis Testing
  10. Geometric Models
  11. Bernoulli Trials
  12. Finite Sampling Models
  13. Games of Chance
  14. The Poisson Process
  15. Renewal Processes
  16. Stochastic Processes
  17. Markov Processes
  18. Brownian Motion

Ancillary Materials

Support and Navigation


Random (formerly Virtual Laboratories in Probability and Statistics) is a website devoted to probability, mathematical statistics, and stochastic processes, and is intended for teachers and students of these subjects. The site consists of an integrated set of components that includes expository text, interactive web apps, data sets, biographical sketches, and an object library. Please read the Introduction for more information about the content, structure, mathematical prerequisites, technologies, and organization of the project. Random is hosted at two sites: www.math.uah.edu/stat/ and www.randomservices.org/stat/. For updates, please follow @randomservices on Twitter.

Technologies and Browser Requirements

This site uses a number of advanced (but open and standard) technologies, including HTML5, CSS, and JavaScript. To use this project properly, you will need a modern browser that supports these technologies. The latest versions of Chrome, Firefox, Opera, and Safari are the best choices. The Internet Explorer and Edge browsers for Windows do not fully support the technologies used in this project.

Display of mathematical notation is handled by the open source MathJax project.

Support and Partnerships

This project was partially supported by a two grants from the Course and Curriculum Development Program of the National Science Foundation (award numbers DUE-9652870 and DUE-0089377). This project is also partially supported by the University of Alabama in Huntsville. Please see the support and credits page for additional information.

Rights and Permissions

This work is licensed under a Creative Commons License. Basically, you are free to copy, distribute, and display this work, to make derivative works, and to make commercial use of the work. However you must give proper attribution and provide a link to the home site: www.math.uah.edu/stat/. Click on the Creative Commons link above for more information.


Mathematics ... is indispensable as an intellectual technique. In many subjects, to think at all is to think like a mathematician.Robert M. Hutchins, The Learning Society