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 such as 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, some 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)
Assignments
Assignment 01 (Due September 09)
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