STAT310: Introduction to Probability and Mathematical Statistics II, Fall 2025

This course introduces the principles and mathematical foundations of statistical reasoning. Topics include samples and populations, estimation, hypothesis testing, analysis of variance, regression, nonparametric procedures, Bayesian methods, and the delta method.

  Instructor: Keith Levin, kdlevin | at | wisc | dot | edu
TA:       Qilin Li, qli478 | dot | xiong | at | wisc | dot | edu
Lectures:
      TuTh, 2:30pm-3:45pm in Engineering Hall 2535
Office Hours:
      Keith Levin: Tuesdays 1pm-2pm, Thursdays 4pm-5pm in 6567 Morgridge Hall or by appointment
      Qilin Li: Tuesdays, 4pm-6pm in 6567 Morgridge Hall
Textbook: Mathematical Statistics and Data Analysis, 3rd Edition by John A. Rice
Syllabus: available here
Prerequisites: at least one one of STAT/MATH 309, STAT 311, STAT/MATH 431, or MATH 531 and at least one of STAT 240, STAT 301, STAT 302, STAT 324, STAT 371, or ECON 310.

Date Topics Readings Notes
Thursday, Sep 4 Course introduction; Administrivia; Probability Review Rice Chapters 1 through 5 (recommended); Probability review notes from Prof. Moulinath Bannerjee (recommended)
Tuesday, Sep 9 Limit Theorems: law of large numbers Rice 5.1-5.2 (recquired)
Thursday, Sep 11 Limit Theorems: central limit theorem Rice 5.3 (required)
Tuesday, Sep 16 Sampling Rice Chapter 7, sections 7.1 through 7.3 (required)
Thursday, Sep 18 Sampling (cont'd) Rice Chapter 7, sections 7.1 through 7.3 (required)
Tuesday, Sep 23 Estimation Rice Chapter 8, sections 8.1 through 8.5 (required)
Thursday, Sep 25 Estimation (cont'd) Rice Chapter 8, sections 8.1 through 8.5 (required)
Tuesday, Sep 30 Estimation (cont'd) Rice Chapter 8, section 8.7 and 8.8 (required)
Thursday, Oct 2 Estimation (cont'd) Rice Chapter 8, section 8.7 and 8.8 (required)
Tuesday, Oct 7 Estimation (cont'd) Rice Chapter 8, section 8.1 through 8.5, 8.7-8.8 (required)
Thursday, Oct 9 Distributions derived from the normal Rice Chapter 6 (required)
Tuesday, Oct 14 Distributions derived from the normal Rice Chapter 6 (required)
Thursday, Oct 16 Exam 1 (in class)
Tuesday, Oct 21 Hypothesis testing Rice Chapter 9, sections 9.1 through 9.4 (required)
Thursday, Oct 23 Hypothesis testing (cont'd) Rice Chapter 9, sections 9.1 through 9.4 (required)
Tuesday, Oct 28 Hypothesis testing (cont'd) Rice Chapter 9, sections 9.1 through 9.4 (required)
Thursday, Oct 30 Hypothesis testing (cont'd) Rice Chapter 9, sections 9.1 through 9.4 (required)
Tuesday, Nov 4 Hypothesis testing (cont'd) Rice Chapter 11, sections 11.1 and 11.2 (required)
Thursday, Nov 6 Hypothesis testing (cont'd) Rice Chapter 11, sections 11.3 and 11.4 (required)
Tuesday, Nov 11 ANOVA: one-way layout Rice Chapter 12, sections 12.1 and 12.2 (required)
Thursday, Nov 13 Exam 2 (in class)
Tuesday, Nov 18 ANOVA: one-way layout and two-way layout Rice Chapter 12, sections 12.1 through 12.3 (required)
Thursday, Nov 20 Regression Rice Chapter 14, sections 14.1 and 14.2
Tuesday, Nov 25 Special topic (TBA) This lecture is intended as an introduction to an important area of modern statistics. You will not be responsible for material presented in this lecture or its readings.
Thursday, Nov 27 No lecture: Thanksgiving break Alice's Restaurant (recommended)
Tuesday, Dec 2 Regression Rice Chapter 14, sections 14.1 and 14.2
Thursday, Dec 4 Regression (cont'd) Rice Chapter 14, sections 14.1 and 14.2
Tuesday, Dec 9 Exam 3 (in class)