2.1 Summary

This week will be a whirlwind recap and review of probability and random variables. In a perfect world, you would have already learned most of if not all of this content already. Because this week is mostly review, it will be a lot of content.

2.2 Learning Objectives

After completing this week, you are expected to be able to:

• Use basic rules of probability including Bayes’ Theorem.
• Understand the definition of a random variable.
• Calculate probabilities given the distribution of a random variable.
• Identify independence and use independence to carry out probability calculations.
• Understand and use conditional and marginal distributions.
• Perform transformations of random variables.
• Use the d*, p*, q* and r* functions for probability calculations in R.

2.3 Reading

2.4 Video

2.5 Assignments

• Homework 01
  • Due: Monday, February 8
  • Submission: Gradescope
  • Solution: Compass

2.6 Office Hours

2.7 Additional Information

• Geyer: Probability Distributions in R
• R Cookbook: Probability
• PSU STAT 414: Distributions of Functions of Random Variables
• The American Statistician: Univariate Distribution Relationships
• Wikipedia: Relationships Among Probability Distributions