Math 4520: Introduction to Mathematical Statistics

Instructor: Sean O'Rourke
Office: Math 325
Office Hours: W: 4:00 pm - 5:00 pm, F: 2:00 pm - 3:00 pm, and by appointment.
E-mail: -
Lectures: MWF: 03:00 pm - 03:50 pm in ECCR 155


We will be using John E. Freund's Mathematical Statistics with Applications (8th Edition) by Miller and Miller.

Course Description

Mathematical statistics is a theoretical and mathematically rigorous approach to understanding the probability needed to do statistics. While this course is an introduction to the subject, it assumes that you already understand the basics of probability.

This semester we will examine point and confidence interval estimation, method of moments, method of maximum likelihood, sufficiency, completeness, and uniformly minimum variance unbiased estimation. In addition, we will study tests for simple and composite hypotheses, including uniformly most powerful tests and likelihood ratio tests. This is more or less the second half of the text.


Your grade in this course will be based on the following:



Every week you will have a written homework assignment, which will give you an opportunity to use the concepts, definitions, theorems and techniques we have learned. These will be posted on the course website. Late homework will not be accepted without proper documentation (such as a doctor's note) or prior approval of the instructor.

Homework should be legible, have your name on it, and be stapled in order to ensure that you get credit. A goal of this course is for you to improve your ability to write clear, precise mathematical arguments; the homework (and the exams) will be graded accordingly.

I encourage you to discuss the homework problems with your classmates, tutors, or me (or any other resources you find helpful). However, the Honor Code requires that the solution you turn in must be in your own words and reflect your own understanding.


Each week you will be assigned reading assignments from the text. You will then complete some online questions (known as warm-ups) based on the reading. Each warm-up assignment is based on 2-4 conceptual questions. These questions serve as preparation for the following lecture and are due one hour before the next class meeting.

Graduate Credit

If you are registered for the graduate level of this course (STAT or MATH 5520), you will have extra homework problems on each assignment, additional take home parts for both midterms, and will generally be held to higher standards for grading.

Homework Assignments

Course policies

Accommodation for Disabilities

If you qualify for accommodations because of a disability, please submit your accommodation letter from Disability Services to your faculty member in a timely manner so that your needs can be addressed. Disability Services determines accommodations based on documented disabilities in the academic environment. Information on requesting accommodations is located on the Disability Services website. Contact Disability Services at 303-492-8671 or for further assistance. If you have a temporary medical condition or injury, see Temporary Medical Conditions under the Students tab on the Disability Services website.

Classroom Behavior

Students and faculty each have responsibility for maintaining an appropriate learning environment. Those who fail to adhere to such behavioral standards may be subject to discipline. Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with race, color, national origin, sex, pregnancy, age, disability, creed, religion, sexual orientation, gender identity, gender expression, veteran status, political affiliation or political philosophy. Class rosters are provided to the instructor with the student's legal name. I will gladly honor your request to address you by an alternate name or gender pronoun. Please advise me of this preference early in the semester so that I may make appropriate changes to my records. For more information, see the policies on classroom behavior and the Student Code of Conduct.

Honor Code

All students enrolled in a University of Colorado Boulder course are responsible for knowing and adhering to the Honor Code. Violations of the policy may include: plagiarism, cheating, fabrication, lying, bribery, threat, unauthorized access to academic materials, clicker fraud, submitting the same or similar work in more than one course without permission from all course instructors involved, and aiding academic dishonesty. All incidents of academic misconduct will be reported to the Honor Code (; 303-492-5550). Students who are found responsible for violating the academic integrity policy will be subject to nonacademic sanctions from the Honor Code as well as academic sanctions from the faculty member. Additional information regarding the Honor Code academic integrity policy can be found at the Honor Code Office website.

Sexual Misconduct, Discrimination, Harassment and/or Related Retaliation

The University of Colorado Boulder (CU Boulder) is committed to fostering a positive and welcoming learning, working, and living environment. CU Boulder will not tolerate acts of sexual misconduct (including sexual assault, exploitation, harassment, dating or domestic violence, and stalking), discrimination, and harassment by members of our community. Individuals who believe they have been subject to misconduct or retaliatory actions for reporting a concern should contact the Office of Institutional Equity and Compliance (OIEC) at 303-492-2127 or Information about the OIEC, university policies, anonymous reporting, and the campus resources can be found on the OIEC website.

Please know that faculty and instructors have a responsibility to inform OIEC when made aware of incidents of sexual misconduct, discrimination, harassment and/or related retaliation, to ensure that individuals impacted receive information about options for reporting and support resources.

Religious Holidays

Campus policy regarding religious observances requires that faculty make every effort to deal reasonably and fairly with all students who, because of religious obligations, have conflicts with scheduled exams, assignments or required attendance. In this class, notify me as early as possible and at least one week before the holiday in order to reschedule any exams or assignments. See the campus policy regarding religious observances for full details.

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