Stats 117: Introduction to Probability

Instructor

Professor John Duchi, CoDa 244E.

• Office hours: Fridays, 10:30 – 12:00, Sequoia 126

Teaching Assistants

Will Hartog

• Office hours: TBD

Jack Krew

• Office hours: TBD

Qizhong Zhang

• Office hours: TBD

Bryan Park

• Office hours: TBD

Ran Xie

• Office hours: TBD

Prerequisites

Students in this class should have a strong knowledge of single variable integral and differential calculus, including understanding of infinite series and related limits. Math 21 or Calculus BC provide sufficient background. If you do not have this, please discuss with Professor Duchi.

Course communication, questions

• The course staff email address is stats117-spr2526-staff@lists.stanford.edu. Please do not use the instructor's or TAs’ direct email addresses for matters related to the course.

• We will use https:edstem.orguscourses97454discussion this quarter for answering questions, finding collaborators, and other course-related things. You should be automatically signed up if you are enrolled in the course.

• We will use Gradescope for accepting assignments.

Course Overview

In this course, we will cover the basic tools of probability, with an eye to allowing students to apply the ideas in other applications and areas. Our topics will begin with counting and progress from there, where we will cover the axioms of probability from which everything else follows. From here, we will discuss random variables (what we think of as “random”), independence and conditional probability, expectations, and a number of common distributions that appear throughout the sciences. At the most holistic level, these tools form the basis for how we decide what is true: how likely is some scientific phenomenon to be, given observations we have made?

Outline

Each of the times for a given topic below is approximate, but we should roughly cover the following:

• Counting and sets (1 week)

• Axioms of probability (1 week)

• Independence and conditional probability (1 week)

• Random variables (2 weeks)

• Joint distributions and multiple random variables (2 weeks)

• Continuous random variables (2 weeks)

Grading

Your grade will be determined by weekly problem sets, either submitted for a grade or presented orally in tutorial sections (20%), a midterm (30%), and an in-person final exam (50%). We reserve the right to change the relative weighting of these at any time. You must take the final exam. Please double check the final exam schedule, and do not leave Stanford before the final is complete. Our final will be on Tuesday, June 9, 8:30 – 11:30 AM.

There will be weekly homework assignments throughout the course, which will count for 20% of the grade. In effort to speed grading and homework return to you, we will grade homework problems and their sub-parts on a {0, 1, 2}-scale: 0 indicates a completely incorrect answer, 1 indicating approximately halfway correct, 2 indicating more or less correct. You are welcome to collaborate on these problem sets, but please acknowledge your collaborators. We will not police LLM usage in this class, but recognize that using an LLM will likely impede your ability to complete the midterm and final well.

Proctoring and OAE

Proctoring pilot

• This course is participating in the proctoring pilot overseen by the Academic Integrity Working Group (AIWG). The purpose of this pilot is to determine the efficacy of proctoring and develop effective practices for proctoring in-person exams at Stanford. To find more details on the pilot or the working group, please visit the AIWG webpage.

Office of Accessible Education

If you plan to use your OAE approved exam accommodations for a specific assessment, you must provide your accommodation letter and inform the teaching staff stats117-spr2526-staff@lists.stanford.edu by

• 10 calendar days prior to the midterm date

• No later than May 25th, 2026, at 5:00 pm for all Spring final exams.

You only need to submit your letter once per quarter. For urgent OAE-related accommodation needs that arise after the deadline, please consult your OAE adviser. If you are not yet registered with OAE, contact the office directly at oae-contactus@stanford.edu.