Mathematical Statistics I

My Current Teaching @ National Tsing Hua University

Fall 2026, Instructor 

• 數理統計一 (Mathematical Statistics I) (QF 314800)

  • Course Description & Audience: This course concentrates on theoretical statistics, using the first principles of probability theory. Our aim is to introduce key fundamentals and lay a solid foundation for students to explore areas such as quantitative finance, data science, statistical signal processing, machine learning, financial mathematics, and econometrics. Many results will be presented in a definition-theorem-proof format. Prerequisites include one year of multivariate calculus. To succeed in this course, a certain level of mathematical maturity is expected. The intended topics to cover are listed below:

    • Introduction to Statistics

    • Probability Theory

    • Transformation and Expectations

    • Common Families of Distributions

    • Multiple Random Variables

    • Sampling Distributions and Random Sample

    • Limiting Behaviors and Central Limit Theorem

    • Elementary Statistical Inferences 

Prerequisites: Students planning to take this course should be fairly familiar with multivariate calculus. As mentioned previously, this course requires strong mathematical maturity to succeed.

Time and Place: Lectures are at T7T8T9, Room 104, TSMC Building. 

Office Hours: The instructor's office is open Monday from 12:00 to 13:00 in Room 608 of the TSMC Building (台積館). Meetings are also possible at other times by appointment.

Textbooks & References: Students will be provided with significant handout material to support the lectures at no cost.  The material is mainly drawn from the following recommended textbooks.

• G. Casella and R. L. Berger, Statistical Inference, Cengage Learning, 2001.

• R. Hogg, J. McKean, A. Craig, Introduction to Mathematical Statistics, Pearson, 2018.

• J. A. Rice, Mathematical Statistics and Data Analysis, Cengage Learning, 2006

• D. Wackerly, W. Mendenhall, and R. L. Scheaffer, Mathematical Statistics with Applications, Thomson Brooks/Cole, 2026.

Teaching Method: Lecture.

Teaching Assistant: Siang Dai (戴翔) (dairyan930128@gmail.com) & Yun-Chi Hsu (許允齊) (star930302@gmail.com).  
TA's office hours: Friday 1-2 PM and 2-3 PM. (TSMC Room 505)

Homework: Approximately weekly. 

Grading: The grade will be based on one midterm test (30%), homework (20%), and a final exam (50%). The instructor may exercise discretion of up to 10% in each grading category.

AI Teaching Assistant:

Gemini Gems (Math Stats Tutor, test version) : 

https://gemini.google.com/gem/1QrhLPcZ6CkL6w-lZ7-3YMJYAzCunS2RK?usp=sharing

AI Teaching Assistant — Terms of Use: The link above is for enrolled students of this course only; please do not redistribute it. To use it, sign in with your Google account (your NTHU Google account is recommended). AI responses are for learning reference and may contain errors — the lecture notes and in-class material take precedence. Do not enter personal or sensitive information in your conversations.

Course Schedule

• Week 01 (09/08)

  • Review of Basic Probability Theory I

• Week 02 (09/15)

  • Review of Basic Probability Theory II

• Week 03 (09/22)

  • Transformation and Expectations I. CDF techniques

• Week 04 (09/29)

  • No Official Class. TA Session Only

  • No official lecture will be held on Tuesday, 09/29. Instead, our TAs will hold a review session to cover selected assignments and related key concepts.

  • Transformation and Expectations II. Expected Value and Variance

• Week 05 (10/06)

  • Transformation and Expectation III: Moment Generating Functions

  • Multiple Random Variables I: Joint Distributions, Marginal Distributions, Expectations

• Week 06 (10/13)

  • Multiple Random Variables: Conditional Distributions and Expectation

• Week 07: 10/20

  • Multiple Random Variables

• Week 08: 10/27

  • Midterm 1

• Week 09: 11/03

  • Review of Midterm 1.

  • Multiple Random Variables IV

• Week 10: 11/03

  • Random Samples: 

• Week 11: 11/17

  • Random Samples II: Cochran Theorem; Order Statistics

• Week 12: 11/24

  • Limiting Behaviors I: Convergence in Probability; WLLN 

• Week 13: 12/01

  • Limiting Behaviors II: Almost Sure Convergence; SLLN 

• Week 14: 12/08

  • Limiting Behaviors III: Convergence in Distribution; CLT

• Week 15: 12/15

  • No Class.

  • Review the Course

  • Course Evaluation

• Week 16: 12/22 

  • Final Exam

Lecture Handouts

• Chapter 1: Basic Probability Theory 

• Chapter 2: Transformation and Expectations 

• Chapter 3: Common Families of Distributions

• Chapter 4: Multiple Random Variables 

• Chapter 5: Random Samples

• Chapter 6: Limiting Behaviors 

Assignments

• Assignment 01 (Due 09/15)

• Assignment 02 (Due 09/22)

• Assignment 03 (Due 09/29)

• Assignment 04 (Due 10/13)

Exam

• Midterm:  Everything up to Chapter 4.5.

• Final Exam:  Chapter 1 to Chapter 6.

Supplementary Documents

• Mathematics Premier for Introduction to Mathematical Statistics by Prof. J. McKean 

• ChatGPT, https://openai.com/blog/chatgpt/ OpenAI

• Claude, https://claude.com/ Anthropic 

• Gemini, gemini.google.com/ Google