What is the Law of Iterated Expectations?

What is the Law of Iterated Expectations?

Approach: Define the relationship between marginal and conditional expectations.

Also known as the Tower Property, it states that the expected value of the conditional expected value of a random variable is the same as the expected value of the variable itself: E[X] = E[E[X|Y]].

Follow-up: How is this used in martingale theory?

Key concepts: tower property, random variables.