Random Variables - Great Expectations to Bell Curves

Massive Open Online Course
  • Overview
  • Course Content
  • Requirements & Materials

Random Variables - Great Expectations to Bell Curves

Course Description

This course discusses properties and applications of random variables. When you’re done, you’ll have enough firepower to undertake a wide variety of modeling and analysis problems; and you’ll be well-prepared for the upcoming statistics courses.

We’ll begin by introducing the concepts of discrete and continuous random variables. For instance, how many customers are likely to arrive in the next hour (discrete)? What’s the probability that a lightbulb will last more than a year (continuous)?

We’ll learn about various properties of random variables such as the expected value, variance, and moment generating function. This will lead us to a discussion of functions of random variables. Such functions have many uses, including some wonderful applications in computer simulations.

If you enjoy random variables, then you’ll really love joint (two-dimensional) random variables. We’ll provide methodology to extract marginal (one-dimensional) and conditional information from these big boys. This work will enable us to study the important concepts of independence and correlation.

Along the way, we’ll start working with the R statistical package to do some of our calculations and analysis.

Course Content



Requirements & Materials



  • Introductory knowledge of theory and basic calculus, as well as the material from the first course in this series (A Gentle Introduction to Probability).
  • Prior experience in Excel, or similar application.



  • Internet connection (DSL, LAN, or cable connection desirable)
  • Adobe Acrobat PDF reader (to download for free, visit get.adobe.com/reader/)
  • R statistical software (to download for free, visit cran.r-project.org) (or similar statistics packages such as Minitab, JMP, SAS, etc.)
  • Excel (or equivalent)
  • Bonus software:  Any “real,” high-level language such as MATLAB, Python, etc.


  • All content and course materials available online

Who Should Attend

This course is designed for anyone who needs the tools to understand data, science, philosophy, engineering, economics, and finance.

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What You Will Learn

  • Discrete and continuous probability random variables
  • The properties of distribution random variables such as the expected value, variance, and moment generating function
  • Functions of random variables and how they can be used in computer simulation applications
  • Joint (two-dimensional) random variables and how to extract marginal (one-dimensional) and conditional information from them
  • The concepts of independence and correlation
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How You Will Benefit

  • Work with the R statistical package.
  • Get introduced to discrete and continuous random variables.
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