SDS 4020 Mathematical Statistics

Course description

This course develops the mathematical foundations of statistical inference. Topics include special and sampling distributions; point estimation; bias, mean squared error, and consistency; confidence intervals; hypothesis testing; order statistics; asymptotic convergence; maximum likelihood; Fisher information and the Cramér–Rao bound; likelihood-ratio methods; sufficiency and completeness; minimum-variance unbiased estimation; and uniformly most powerful tests. Bayesian estimation, linear models, or related topics may be included as time permits.

Prerequisites and materials

Prerequisites

Math 493, Math 3200, and Math 318 (or Math 308), or equivalent mathematical maturity and experience.

Textbook

Robert V. Hogg, Joseph W. McKean, and Allen T. Craig, Introduction to Mathematical Statistics, 8th ed., Pearson, 2018. Solutions to selected exercises appear in the back of the book.

Software

We will use the open-source statistical software R and, optionally, RStudio Desktop. Any required code or data will be distributed through Canvas or the course site.

Coursework and exams

Homework

Approximately 11 assignments will be given during the semester, generally with about six problems each and occasional computational work. Unless an assignment states otherwise, homework is due Wednesday at 11:59 p.m. Central Time. Solutions will be posted after submission closes, and students should compare their work with the posted solutions when studying.

Routine late submissions are not accepted. Students with an approved accommodation or a documented emergency should contact the instructor as soon as possible.

Exams

There will be one midterm and one cumulative final. Exams are closed book and closed notes, except that each student may bring one letter-size sheet of notes, written on both sides. Needed distribution tables will be provided. Calculators are allowed unless different instructions are announced for a particular exam.

• Midterm: Tuesday, October 13, 2026, 11:30 a.m.–12:50 p.m., MCMILLAN 0G052.
• Final exam: university final-exam period, December 10–16; exact assignment to be announced by the registrar.

Make-up exams are reserved for documented conflicts, university-approved accommodations, or emergencies. Notify the instructor before the exam whenever possible; in an emergency, make contact promptly and provide documentation within two business days. A make-up will ordinarily be completed within one week of the scheduled exam.

Grading

Letter-grade thresholds: A ≥ 92; A− 90–<92; B+ 88–<90; B 82–<88; B− 80–<82; C+ 78–<80; C 72–<78; C− 70–<72; D+ 68–<70; D 62–<68; D− 60–<62; F < 60.

An A+ may be awarded for exceptional performance. Course scores will be compared with these fixed thresholds without individual rounding or grade adjustments. Any clarification to the grading scale will be announced in writing and applied consistently to the entire class.

Course policies and student support

Collaboration, academic integrity, and AI

Students may discuss concepts and general approaches on homework, but each student must write and submit their own solutions and code and must acknowledge substantive help. Unless an assignment explicitly permits it, generative AI may not be used to produce or substantially revise work submitted for credit. Exams must be completed independently using only the materials authorized for that exam. All work is subject to Washington University’s Academic Integrity Policy.

Accessibility and accommodations

Students seeking disability-related accommodations should work with Disability Resources and share their accommodation letter with the instructor. Please arrange a conversation early so that approved accommodations, including exam arrangements, can be implemented effectively.

Religious observance and other university-approved absences

Notify the instructor in writing as early as possible—ideally by the end of the third week of class—about a religious observance or other university-approved absence that conflicts with coursework or an exam. Reasonable arrangements will be made without academic penalty.

Learning and well-being

Students may consult the university’s Campus Resources page for Disability Resources, the Learning Center, the Writing Center & Speaking Studio, and well-being support. If circumstances are affecting your work, contact the instructor early so available options can be discussed.

Changes to this syllabus

The instructor may adjust the topic sequence, homework pacing, or other details to support learning. University holidays and the announced midterm date are fixed; any other change will be announced in Canvas and reflected on the course schedule.