Introduction to Probability

Course information

  • Quarter: Fall 2026.
  • Lecture time: Wednesdays and Fridays, 1:30-2:50pm.
  • Quiz time: Mondays beginning October 5; arrive by 1:30pm, quiz from 1:45-2:05pm.
  • Final exam: Wednesday, December 9, 3:30-6:30pm; location TBD.
  • Lecture and quiz location: TBD.
  • Course platforms: Canvas and Ed.
  • Prerequisites: CME 100 or MATH 51.

Description

Probability is the foundation behind many important disciplines, including statistics, machine learning, risk analysis, stochastic modeling, and optimization. This course provides an in-depth undergraduate-level introduction to fundamental ideas and tools of probability. Topics include the foundations (sample spaces, random variables, probability distributions, conditioning, independence, expectation, variance), a systematic study of the most important univariate and multivariate distributions (Normal, Multivariate Normal, Binomial, Poisson, etc…), as well as a peek at some limit theorems (basic law of large numbers and central limit theorem).

Learning goals

Through active engagement and completion of course activities, you will be able to work with randomness and uncertainty in diverse application domains by employing probabilistic reasoning. This will involve understanding:

  • The random variables that are most widely used to model randomness throughout science and engineering,
  • Paradoxes and common pitfalls when applying probabilistic reasoning, and
  • How to update probabilistic models based on new information and experimental data.

Course structure

This course will be facilitated through in-person lectures, quizzes, and tutorials. All assignments will be posted on Canvas. Announcements will also be made through Canvas, and questions should be posted to Ed. Please use a private Ed post for personal matters.

  • Lecture: Lectures will be held on Wednesdays and Fridays from 1:30-2:50 PM.
  • Homework: Homework will not be collected or graded, but completing it is highly recommended as preparation for the weekly quizzes and tutorials.
  • Quizzes: Each quiz will consist of one question closely related to the previous week’s (ungraded) homework. Students should arrive by 1:30 PM so they have time to use the restroom and get settled. Quizzes will begin promptly at 1:45 PM and end at 2:05 PM. Students who arrive after 1:45 PM will not be permitted to take the quiz. Quizzes are closed-book and closed-note, and calculators are not permitted. A course-provided “cheat sheet” for each quiz will be linked from the corresponding entry on the Schedule page and may be used during the quiz.
  • Tutorials: Tutorials begin in the third week of the quarter (the week of October 5). Each student will be assigned to one half-hour-long weekly tutorial with two or three other students and one CA. The CA will guide the students through several practice problems. Tutorials are closed-book and closed-note, and calculators are not permitted. Each tutorial will be graded as follows:
    • 4/4 — Participates: Arrives prepared, having reviewed the lecture materials and the (ungraded) homework from the previous week; participates and tries the new material.
    • 1/4 — Unprepared or does not participate: Attends but is unprepared or does not participate.
    • 0/4 — Does not attend.

Course materials

  • Required textbook: Blitzstein, J. & Hwang, J. (2019). Introduction to Probability (2nd edition).
    You can access it for free here.
  • Course reader
  • Optional textbook: Ross, Sheldon M. (2014). A first course in probability.
    Available at Stanford’s library.