Chapter 1 M1: Probability

In this module we take a speedy trip through probability concepts that will be important to us in this course. Some of these topics will (I hope) be review for you, but pay attention to things like notation variations and re-using ideas in new contexts. Depending on where and when you took your probbility prerequisite, you may or may not have seen MGFs before :)

Learning goals for this module include:

• Work with conditional, joint, and marginal distributions:
  • Define what those are
  • Convert between them if you’re given sufficient information
• Work with moments of random variables (and combinations thereof!)
  • Describe what moments are and what they tell you about a distribution
  • Use probability rules about what happens to moments (and MGFs!) if you take linear combinations of random variables
  • Find a distribution’s moments – using the definition, probability rules, and moment-generating functions