Probability: Random Variables

By the end of this module, learners should be able to:

  • Name situations in which randomness is used or occurs naturally,
  • State properties of valid probability mass and density functions, including how they can be used to quantify uncertainty about random outcomes,
  • Distinguish between discrete and continuous random variables and between probability mass and probability density functions,
  • Identify situations in which it is appropriate to use uniform, Bernoulli, binomial, and normal probability models,
  • Differentiate between mean and variance for data and for random variables, applying appropriate notation, and describe how they are connected through the Law of Large Numbers,
  • Calculate mean and variance for finite discrete random variables,
  • Apply properties of expectation and variance to find the expectation and variance of the average of independent random variables,
  • State the properties of normal distributions, including their relationship to the standard normal distribution,
  • Use normal quantile plots to assess whether data appear to be observations from a normal distribution.

Topics covered in this module

Expected time to complete the learning resources in this module: 3 hours.

Learning resources:

  1. Introduction to Probability:  Random Variables ‎(video)
  2. Discrete Random Variables (video)
  3. Bernoulli and Binomial Random Variables (video)
  4. Expected Value and Variance (videos)
  5. Probabilities for Continuous Random Variables (video)
  6. Normal Distributions (videos)
  7. Guide to carrying out the analysis in the module using R (pdf)
  8. Guide to carrying out the analysis in the module using SPSS (pdf)