Course: Math 408, Mathematical Statistics, Fall 2023
Prerequisite: Math 407, Probability Theory.
Course Content: Principles for testing hypotheses and estimation, confidence intervals, methods of moments, maximum likelihood, information inequality, likelihood ratio tests, goodness of fit and nonparametric methods.
Last update: 9 May 2023

Instructor: Steven Heilman, stevenmheilman(@-symbol)
Office Hours: Tuesdays, 9AM-11AM, on zoom [link posted in blackboard]
Lecture Meeting Time/Location: Mondays, Wednesdays, and Fridays, 1PM-150PM, KAP 156
TA: Tianle Liu, tianleli(@-symbol)
TA Office Hours: Held in the Math Center, with schedule provided at that link.
Discussion Section Meeting Time/Location:

Textbook: The following textbook is recommended but not required.
Rice, Mathematical Statistics & Data Analysis.

Exam 1: Wednesday, September 27, 1PM-150PM, KAP 156
Exam 2: Friday, November 3, 1PM-150PM, KAP 156
Final Exam: Wednesday, December 13, 11AM-1PM, Location TBD
Other Resources: Supplemental Problems from the textbook. An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments

Email Policy:

Exam Procedures: Students must bring their USCID cards to the midterms and to the final exam. Phones must be turned off. Cheating on an exam results in a score of zero on that exam. Exams can be regraded at most 15 days after the date of the exam. This policy extends to homeworks as well. All students are expected to be familiar with the USC Student Conduct Code. (See also here.)
Accessibility Services: If you are registered with accessibility services, I would be happy to discuss this at the beginning of the course. Any student requesting accommodations based on a disability is required to register with Accessibility Services (OSAS) each semester. A letter of verification for approved accommodations can be obtained from OSAS. Please be sure the letter is delivered to me as early in the semester as possible. OSAS is located in 301 STU and is open 8:30am-5:00pm, Monday through Friday.
213-740-0776 (phone)
213-740-6948 (TDD only)
213-740-8216 (fax)

Discrimination, sexual assault, and harassment are not tolerated by the university. You are encouraged to report any incidents to the Office of Equity and Diversity or to the Department of Public Safety This is important for the safety whole USC community. Another member of the university community - such as a friend, classmate, advisor, or faculty member - can help initiate the report, or can initiate the report on behalf of another person. The Center for Women and Men provides 24/7 confidential support, and the sexual assault resource center webpage describes reporting options and other resources.

Exam Resources: Here are exams from the last time I taught 408: Exam 1 Exam 1 Solution Exam 2 Exam 2 Solution Final Final Solution. Some past 408 exams appear here, near the bottom of the page. Some practice exams for a course similar to ours appear here, here, and here

Homework Policy:

Quiz Policy

Grading Policy:

Tentative Schedule: (This schedule may change slightly during the course.)

Week Monday Tuesday Wednesday Thursday Friday
1 Aug 21: Review of Probability Aug 22 Aug 23: 5.3, Review of Probability Aug 24: Homework 1 due Aug 25: 6.2, 6.3, Review of Probability
2 Aug 28: 7.3, Review of Probability Aug 29 Aug 30: 8.1, 8.2, Parameter Estimation Aug 31: Quiz 1 Sep 1: 8.3, Parameter Estimation
3 Sep 4: No class Sep 5 Sep 6: 8.4, Method of Moments Sep 7: Homework 2 due Sep 8: 8.5, Maximum Likelihood Estimation
4 Sep 11: 8.6, Efficiency, Cramer-Rao Sep 12 Sep 13: 8.7, Sufficiency, Rao-Blackwell Sep 14: Quiz 2 Sep 15: 9.1, 9.2, Hypothesis Testing
5 Sep 18: 9.2, Likelihood Ratio Tests Sep 19 Sep 20: 9.3, Neyman-Pearson Lemma Sep 21: Homework 3 due Sep 22: 9.4, Confidence Intervals
6 Sep 25: 9.4, Confidence Regions/Hypothesis Tests Sep 26 Sep 27: Exam 1 Sep 28: No homework due Sep 30: 9.4, p-values
7 Oct 2: 9.5, Generalized Likelihood Ratio Test Oct 3 Oct 4: 8.2, Case Study: Alpha Particles, Contingency Tables Oct 5: Quiz 3 Oct 6: 8.2, Case Study: Alpha Particles, Contingency Tables
8 Oct 9: 8.2, Case Study: Alpha Particles, Contingency Tables Oct 10 Oct 11: 11.2, Comparing Independent Gaussians Oct 12: Homework 4 due,No class Oct 13: No class 
9 Oct 16: 11.2, Comparing Independent Samples Oct 17 Oct 18: 11.2, Comparing Independent Samples Oct 19: Quiz 4 Oct 20: 11.3, Comparing Dependent Samples
10 Oct 23: 12.2, Analysis of Variance Oct 24 Oct 25: 12.2, Analysis of Variance Oct 26: Homework 5 due Oct 27: 14.2, Linear Regression
11 Oct 30: 14.2, Linear Regression Oct 31 Nov 1: 14.2, Linear Regression Nov 2: No homework due Nov 3: Exam 2
12 Nov 6: 14.3, 14.4, Least Squares Nov 7 Nov 8: 14.3, 14.4, Least Squares Nov 9: Quiz 5 Nov 10: No class
13 Nov 13: Leeway Nov 14 Nov 15: Leeway Nov 16: Homework 6 due Nov 17: Leeway
14 Nov 20: Leeway Nov 21 Nov 22: No class  Nov 23: No class Nov 24: No class
15 Nov 27: Review of course Nov 28 Nov 29: Review of course Nov 30: Quiz 6 Dec 1: Review of course

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Homework .tex files

Quiz Problems

Exam Solutions

Supplementary Notes