Conditioning

When two random variables are related, learning the value of one can change what we expect to happen with the other.

This idea is called conditioning, one of the most important ideas in probability, statistics, and especially econometrics. Much of econometrics is ultimately about asking what we learn about one variable when we know something about another!

We begin with conditional expectations and how to calculate them, before introducing the law of iterated expectation. We then extend the same ideas to conditional variance and the law of total variance.

These ideas may seem fairly abstract at first, but they will become extremely useful later on!