Chapter 2.2: In this module we focus primarily on how the definition of a pmf comes about from our development of a probability space. The specific examples listed will be deferred to the next module.

In Chapters 2.3-2.5 as well, some of the examples may be unfamiliar, we leave the examples for the next module. In this Chapter, it is more important to focus on how the definitions come about and why they make sense. You shouldn’t have to memorize “formulae” for computing expectations of functions of random variables, or memorize any “property” if you understood the core (what a random is, and how a pmf is induced on a discrete random variable).

Chapter 2.5, appreciating multiple random variables in a single probability space is very important. Pay attention to the running example in class when we explore all these concepts.

In Chapter 4.4, we are only focusing on the definition of the MGF, and to motivate why we look at moments of a random variable.

The next module will reflect the same structure as this, but with specific examples of random variables which are very important.