Statistical Theory & Methods 1 (320-1-22)

Instructors

Arend M Kuyper
IPR, 2040 Sheridan Road, Evanston

Meeting Info

Harris Hall L07: Mon, Wed 9:30AM - 10:50AM

Overview of class

We will develop concepts of probability theory necessary to understand statistical theory. Specific topics to be discussed include sample spaces, probability measures, conditional probability, independence, random variables, distributions, expected values, and limit theory. The sequel (320-2) emphasizes statistical inference.

Registration Requirements

Prerequisites/Corequisites: Introductory Statistics (STAT 202-0, STAT 210-0, or equivalent); Series, Sequences, and Multivariable Integration (STAT 228-0/Math 235-0, or BOTH Math 226-0 AND Math 230-2 — or equivalent courses)

Learning Objectives

1. Construct probability models by defining sample spaces and events, applying the axioms of probability, and using counting techniques.
2. Solve multi-stage problems using conditional probability, the Law of Total Probability, Bayes' rule, and independence.
3. Select a common distribution (e.g., Binomial, Poisson, Exponential, Normal) to model a scenario and justify the choice.
4. Derive distributions of transformed random variables, sums of independent random variables, and order statistics.
5. Analyze relationships among random variables using joint, marginal, and conditional distributions, covariance, and correlation.
6. Calculate expectations, variances, and conditional expectations using linearity and the laws of total expectation and variance.
7. Apply Markov's and Chebyshev's inequalities, the Law of Large Numbers, and the Central Limit Theorem to bound or approximate probabilities.
8. Communicate solutions as clear, logically complete arguments that state assumptions and justify each step.
9. Critique proposed solutions to probability problems by finding and correcting errors in assumptions, reasoning, or calculation.

Teaching Method

The course will use a flipped/blended design, meaning a sizable portion of class time will be dedicated to working on activities and homework/quizzes/mastery problems. A typical class will devote 15- 25 minutes to discussion/lecture, with the remaining time devoted to activities and homework/quizzes/mastery problems where we work together to build a deeper understanding of course materials. Ideally, the first 15-25 minutes of discussion/lecture will be driven by students through the submission of questions or request for clarifications prior to class time - mechanism will be in place to facilitate this process. Given the course design, students will be expected to adequately prepare for each discussion/lecture by reviewing assigned material (e.g. readings, videos, etc.) because class time will be focused on pre-submitted questions and then working on homework/quizzes/mastery problems designed to reinforce understanding of course concepts. Students will be expected to collaborate and engage with other students to solve problems and help each other learn.

Evaluation Method

Students will be evaluated through small assignments, weekly homework assignments, 2 exams, and a final take-home assignment. Other assessment types may also be used at the instructor's discretion.

Class Materials (Required)

The Art of Chance, by Dennis Sun, Gene Kim, and Anav Sood, free online text (https://dlsun.github.io/skis/)
Mathematical Statistics and Data Analysis, 3rd Edition, by John A. Rice, ISBN (Print) 9780534399429, ISBN (digital) 9781111793715, other options are available
Other learning materials will be provided by the instructor

Class Attributes

SoC Mathematics, Science, and Technology Distro

Enrollment Requirements

Enrollment Requirements: Co-requisites: STAT 202-0 or 210-0 or 232-0 or PSYCH 201-0 or IEMS 201-0 or IEMS 303-0 or equivalent, and STAT 228-0 or MATH 235-0 or both MATH 226-0 and 230-2 or MATH 228-2 or 281-2 or 285-3 or 290-3 or 291-3 or ES_APPM 252-2