By the end of this module, you 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
Learning resources:
- Introduction to Probability: Random Variables (video)
- Discrete Random Variables (video)
- Bernoulli and Binomial Random Variables (video)
- Expected Value and Variance (videos)
- Probabilities for Continuous Random Variables (video)
- Normal Distributions (videos)
- Optional: Guide to carrying out the analysis in the module using R (pdf)