STA 257F: Probability and Statistics I, Fall 2025 [TENTATIVE]

This course will present an introduction to mathematical probability theory, including: probability spaces, common probability distributions, discrete and continuous random variables, distribution and density functions, joint distributions, expected values, generating functions, probabilistic inequalities, convergence of random variables, laws of large numbers, the Central Limit Theorem, and the concept of statistical inference. See also the evolving lecture notes, to be updated the evening after each lecture.

Course Web Page Quick link: probability.ca/sta257

Prerequisites: MAT137 or 157 (or their UTSc/UTM equivalents), plus co-requisites MAT237 / 257 and MAT223 / 240. Strictly enforced by the university! (Note: The related courses STA237 and 247 have lower math prerequisites.)

Course Enquiries email address: sta257@course.utoronto.ca   (Or, for enrolment/prerequisite issues: ug.statistics@utoronto.ca.)

Instructor: Professor Jeffrey S. Rosenthal, Department of Statistics, University of Toronto. Email j.rosenthal@math.toronto.edu; web http://probability.ca/jsr

Lectures -- Mondays (2 hours) and Wednesdays (1 hours):
First class Sept 3. Last class Dec 1. No class Oct 13 (Thanksgiving) nor Oct 27 nor 29 (Reading Week).
Lectures will be interactive; please stop talking and put away your phone/laptop (except when being used for the class) and pay close attention to the material being presented, and raise your hand to ask and respond to questions, and participate in polls (info below). You may also be called upon to answer questions, or asked to move forward in the classroom.

Tutorials -- Wednesdays (1 hour, right after lecture -- make sure to REGISTER for one!):
First tutorial Sept 10. Last tutorial Nov 26. No tutorial Oct 29 (Reading Week) nor Nov 12 (Midterm #2).
Tutorials will discuss solutions to each week's suggested homework problems.
TAs will also have some time for office hours, and to reply to email and Piazza questions.
See also the New College Stat Aid Centre (scroll down).

Evaluation:
27% Midterm #1: Mon Oct 6, at 11:10-1:00 for L0101 or 3:10-5:00 for L0201; 100 mins. (See test info.)
27% Midterm #2: Wed Nov 12, at 11:10-1:00 for L0101 or 3:10-5:00 for L0201; 100 mins. (See test info.)
41% Final Exam: to be scheduled some time in Dec 5-23; three hours. (See test info.)
5% Class poll participation. (See poll registration and information here.)
• You can also earn up to three tutorial participation bonus points.

Textbook: We will roughly follow the book Probability and Statistics: The Science of Uncertainty (2nd ed) by M.J. Evans and J.S. Rosenthal, available as a free pdf file of the entire book, specifically the first four chapters:
Chapter 1 (Probability Models, pp. 1-32),
Chapter 2 (Random Variables and Distributions, pp. 33-128),
Chapter 3 (Expectation, pp. 129-198),
Chapter 4 (Sampling Distributions and Limits, pp. 199-252)
• See also the TOC and preface and background and index and answers and solutions manual.
Note: Please try to save these pdf files locally on your computer, rather than download them every time.
[Much of this material is also covered in Chapters 1-4 of this book, with solutions at this link: search ISBN 978-3-319-52401-6, then "product archive file"; see also this book.]
[The follow-up course STA261 then covers much of the material in the later chapters, and STA347/STA447/book expand on probability theory and Chapter 11.]

Homework: There will be suggested homework exercises assigned from the textbook each week, listed within the course notes. They will not be handed in or graded, but they will be discussed in tutorial, and are strongly recommended to learn the material well (and for bonus points). See also the book's selected answers and solutions; send corrections to sta257@course.utoronto.ca. (We will mostly skip the textbook's Challenges and Discussion Topics, but you are encouraged to think about them too.)

Statistical Computing: This course will not require students to perform statistical computations. However, the statistical package "R" will be demonstrated in lecture, and students are encouraged to try it on their own; see this basic R information or textbook Appendix B.

Instructor Office Hours: Monday lectures will end a bit early, and the instructor will stay for questions. He will also (probably -- to be confirmed) have office hours on Wednesdays 2:10-2:45 during term time (but not on midterm days nor Reading Week), in his office [Ontario Power Building, 700 University Avenue, 9th Floor, room 9070; SW Corner of College St and University Ave]. You can also email the instructor to ask questions or arrange to meet. Special additional office hours will be arranged before the midterms and exam and as needed.

Discussion Page: There will be a STA257 "Piazza" discussion page where students can post and answer questions about the course. You should be able to access it from the course's quercus page; let me know of any difficulties. Be sure to keep posts respectful and polite. Also, feel free to lead a recognized study group, or join a drop-in study space or learning community.

Stressed? If you encounter challenges during your studies, then please see these support options or here or visit Learning Support or the Health & Wellness Centre or Navi for assistance and support.



This document is available at probability.ca/sta257, or permanently at probability.ca/jeff/teaching/2526/sta257/.