2.1 Learning Objectives

At the end of this week’s course of study (which includes the async, sync, and homework) students should be able to

1. Remember that random variable are neither random, or variables, but instead that they are a foundational object that we can use to reason about a world.
2. Understand that the intuition developed by the use of set-theory probability maps into the more expressive space of random variables
3. Apply the appropriate mathematical transformations to move between joint, marginal, and conditional distributions.

This week’s materials are theoretical tooling to build toward one of the first notable results of the course, conditional probability. This is the idea that, if we know that one event has occurred, we can make a conditional statement about the probability distribution for another, dependent distribution.