Math 494 Mathematical Statistics

Instructor: Likai Chen (likai.chen[at]

Lectures: 2:00-2:50 p.m on Mondays, Wednesdays, and Fridays in Busch 100

Office hour: Mon 12:00 -1:00 p.m and Wed 3:00 p.m-4:30 p.m. Cupples I Room 107

TA: Peng, Siqi (, Zhou, Tianwei (

TA hour: Monday 4-5 p.m. and Tuesday 10:30-11:30 a.m. Cupples I Room 6 (downstairs)

Grader: Han, Jane (


Topics covered

Special Distributions, theory of estimation, minimum variance and unbiased estimators, maximum likelihood theory, Bayesian estimation, prior and posterior distributions, confidence intervals for general estimators, standard estimators and distributions such as the Student-t and F-distribution from a more advanced viewpoint, hypothesis testing, the Neymann-Pearson Lemma (about best possible tests), linear models, and other topics as time permits.


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


Robert Hogg, Joseph McKean and Allen Craig,
Introduction to Mathematical Statistics, 7th/8th edition
Pearson Prentice Hall, 2018

Solutions to selected problems are in the back of the book.


There will be two midterms and one final. Midterms are in class on 10/04 and 11/15. The final is scheduled 12/16 3:30 p.m.-5:30 p.m. All exams are closed book and closed note. No web-enabled devices may be used. One page (letter size and two-sided) note may be brought to exams. All the distribution tables will be provided by the instructor. Calculators are allowed but not required.

Make-up exams are strongly discouraged. If you are aware of a conflict, please inform the instructor before the exam. Make-up exam will only be given if (1) within 1 week of the standard exam and (2) suitable documentation is provided within 2 days.


There will be about 11 homework assignments throughout the semester. About 6 homework problems (may including computer homework problems) will be assigned each week and the solutions to all problems will be posted on the course website. Most of the exam and final questions will be similar to these. Hence you are strongly suggested to compare your answers with the posted solution. Weekly homework is due on Wednesday midnight. NO LATE HOMEWORK WILL BE ACCEPTED. One lowest grade of your hw will be dropped.

Homework collection via crowdmark: Only PDF and JPEG format are accepted.

You will receive a link in email to submit your homework on crowdmark. After you finish homework, you need to upload your work for each homework question separately. Simply drag and drop your files to the upload areas under the questions or browse to locate them. You can drag pages between questions, and add or delete more pages under each questions. Please DO NOT upload your entire file to all homework questions, but only keep the related pages to each question. If you upload pictures of your homework, please make sure your pictures are sharp enough to be graded. Please ensure the uploaded pages are in order and rotated correctly. After your work is graded, you will receive another link in email to review your score and grading comments.


Your grade will be based on weekly homework, midterm and final exam.

Midterms 25% each
Final 35%
Homework 15%

The threshold for each grade

A A- B+ B B- C + C C -
88 or above85-88 83-85 77-83 75-77 73-75 65-73 60-65
Only very few top students will get A+.


Open-source software R for statistical computing, and its manual .
Download R from Wustl's software.
Download R Studio from its developer's website.