Probability and Statistics

Teaching Semesters

• 2025 Fall, 2024 Fall, 2023 Fall.

Acknowledgement

I gratefully acknowledge Pearson for kindly providing me with complimentary sample copies of their textbooks for my teaching. I appreciate their trust and support. These resources have informed the development of some of my personal teaching materials, which are presented below.

Personal Teaching Materials & Resources

Personal Slides

This version was carefully adapted for my actual lectures, refined to reflect my teaching style and the needs of my students. The modifications include reworded explanations, added examples, exercises, and annotated notes to support classroom use. Copyright © Xiaozhou Li — CC BY-NC-ND 4.0

Note: Minor updates or in-class adjustments may not be reflected here in real time; slides are usually updated after each chapter is completed.

• Course Overview Slide

• Chapter 1. Introduction to Probability Slide
  • 1.1 History of Probability
  • 1.2 Interpretations of Probability
  • 1.3 Experiments
  • 1.4 Set Theory
  • 1.5 The Definition of Probability
  • 1.6 Counting Methods
• Chapter 2. Conditional Probability Slide, Lecture Note
  • 2.1 The Definition of Conditional Probability
  • 2.2 Bayes’ Theorem
  • 2.3 Independent Events
• Chapter 3. Random Variables and Distributions Slide, Lecture Note
  • 3.1 Random Variables and Discrete Distributions
  • 3.2 Continuous Distributions
  • 3.3 The Cumulative Distribution Function
  • 3.4 Bivariate Distributions
  • 3.5 Marginal Distributions
  • 3.6 Conditional Distributions
  • 3.7 Multivariate Distributions
  • 3.8 Functions of a Random Variable
• Chapter 4. Expectation Slide, Lecture Note
  • 4.1 The Expectation
  • 4.2 Variance
  • 4.3 Moments
  • 4.4 Covariance and Correlation

• Chapter 5. Special Distribution Slide

• Chapter 6. Large Random Samples Slide
• Chapter 7. Estimation Slide
• Chapter 8. Sampling Distributions of Estimators Slide
• Chapter 8. Testing Hypotheses Slide

Supplementary Learning Materials

• Problem Sets. A curated collection of problems from my courses, designed to deepen your understanding and sharpen your problem-solving skills.
• More Comprehensive Support：For general study tips, course-specific advice, and academic guidance, you can also refer to my Study Resources & Advice