Mathematical Statistics I

My Current Teaching @ National Tsing Hua University

Fall 2025, 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 many fundamentals and lay a solid foundation for students to explore various areas, including quantitative finance, data science, statistical signal processing, machine learning, financial mathematics, and econometrics in the future. Many of the results will be delivered in a definition-theorem-proof manner. The prerequisite is one year of 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, some mathematical maturity is expected to succeed in this course.

Time and Place: Lectures are at T7T8T9, Room 204 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, 2008.

Teaching Method: Lecture.

Teaching Assistant: 甘容 (Rong Gan), ganzong@gmail.com.  TA's office hours: Friday from 12:00 to 13:00 in Room 505 of the TSMC Building.

Homework: Approximately weekly. 

Grading: The grade will be based on one midterm test (30%), homework (30%), and a final exam (40%). The instructor may exercise discretion up to 10% in each grading category.

Course Schedule

• Week 01 (09/02)

  • Review of Basic Probability Theory I

• Week 02 (09/09)

  • Review of Basic Probability Theory II

• Week 03: 09/16

  • Transformation and Expectations I. CDF techniques

• Week 04: 09/23

  • Transformation and Expectations II. Expected Value and Variance

• Week 05: 09/30

• Week 06: 10/07

• Week 07: 10/14

• Week 08: 10/21

• Week 09: 10/28

• Week 10: 11/04

• Week 11: 11/11

• Week 12: 11/18

• Week 13: 11/25

• Week 14: 12/02

• Week 15: 12/09

• Week 16: 12/16 

  • 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 September 09)

• Assignment 02 (Due September 16)

• Assignment 03 (Due September 23)

• Assignment 04 (Due September 30)

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