MA 481: Mathematical Statistics

Prerequisite: [MA 382 (Introduction to Statistics)] -or- [MA 381 (Introduction to Probability) + instructor consent]

2026-27 Offering: In-person meetings occur on Monday, Tuesday, & Friday at 9am. Thursday's meeting is asynchronous, online.

Degree Requirements: This course can be used, generally, as a technical or mathematics elective. It is also relevant to the following programs:

• Statistics & OR Core for math majors
• Statistics minor
• Validation by Educational Experience (VEE) Mathematical Statistics credit for SOA, CAS,or CIA

Example Syllabus from Winter 2022
Example Topics Schedule from Winter 2022

Here's the pitch...

This course introduces students to the analytical tools needed to establish the properties of common statistical methods. We will answer questions such as:

• Why do sampling distributions of many statistics (including, but not limited to, the sample mean) become bell-shaped with large sample sizes?
• When is the sample mean the best estimator of the population mean?
• What do we mean by best estimator?
• What statistic(s) estimate the population parameter(s) for different estimation techniques?

This class will help prepare students to engage with theoretical statistics literature at an introductory level. If you are considering graduate-level work in statistics, this course is highly recommended and could strongly bolster your grad school application. Students that are interested in actuarial science should also consider this course, as the material is associated with required VEE credit.

To be successful in this course, a strong understanding of introductory probability is required. A first course in statistics is also a requirement so that we can engage with content and eliminate the need for a lengthy review of the basics.

While building a solid foundation for statistical inference, the course makes use of computing as a bridge between classical theory and the modern approaches used to characterize statistical methods.

Learning Objectives

As expected in any statistics course, we emphasize correct usage and interpretation of key statistical terms and concepts. This class also emphasizes the underlying theory of statistical methods and models. Specifically, after taking this course, you will be able to:

• Describe the role of probability theory in statistical inference for a population.
• Compare and contrast modes of convergence and describe their role in sampling distributions.
• Construct a proof to establish a property of an estimator or sequence of random variables.
• Associate a statistical method with various statistical properties such as consistency, unbiasedness, and asymptotic normality.
• Use simulations to demonstrate and supplement theoretical results.