Practice Questions

The following are questions selected to prepare you for the mini-quizzes. Questions are based off of the sections in the textbook and are linked to lectures in the schedule

Note

Ensure you can confidently solve for each problem unassisted (i.e., without the use of Generate AI or by peaking at the solutions. Doing so can give you a false sense of confidence)!

Allow yourself the time and patience to struggle a bit on the questions - it’s great for learning!

And of course, come to office hours if you want extra help, or a dedicated space/time to work through these problems with your peers.

• Section 1.2 (Basic Probability)
• Section 1.3 (Properties of Probability)
• Section 1.4 (Uniform Probabilities on Finite Spaces)
• Section 1.5 (Conditional Probability and Independence)
• Section 2.1 (Random Variables)
• Section 2.2 (Distributions)
• Section 2.3 (Discrete Random Variables)
• Section 2.4 (Continuous Random Variables)
• Section 2.5 (Cumulative Distribution Functions)
• Section 2.6 (Transformations)
• Section 2.7.1 (Joint Distributions)
• Section 2.7.2 (Marginal Distributions and Independence)
• Section 2.8 (Conditional Distributions and Independence)
• Section 3.1 and 3.2 (Expectation)
• Section 3.3 (Variance, Covariance, and Correlation)
• Section 3.4 (Moment Generating Functions)
• Section 3.5 (Conditional Expectation)
• Section 3.6 (Inequalities)
• Section 4.2 (Convergence in Probability)
• Section 4.3 (Convergence Almost Surely (w.p. 1))
• Section 4.4 (Convergence in Distribution)