This section contains our crash course review of topics in probability. The discussion mostly follows Chapter 2 in the Stock and Watson textbook, and I have cross-listed the relevant sections in the textbook here.
At a very high level, probability is the set of mathematical tools that allow us to think about random events.
Just to be clear, random means uncertain, not 50:50.
A simple example of a random event is the outcome from rolling a die.
Eventually, we will treat data as being random draws from some population. Examples of things that we will treat as random draws are things like a person’s hair color, height, income, etc. We will think of all of these as being random draws because ex ante we don’t know what they will be.