Stats 116: Introduction to Probability

Instructor

Professor John Duchi, Sequoia 126.

• Office hours: Tuesdays and Thursdays, 13:15 - 14:15.

Teaching Assistants

• Julie Zhang. Office hours: Wednesdays, 9:00-10:30, Sequoia 220

• Rahul Kanekar. Office hours: Office hours: Mondays, 13:30 - 15:30, Sequoia 207 (Bowker)

Prerequisites

Most students in this class will have a working knowledge of multivariate differential and integral calculus, typically at the level of Math 51 and 52. If you do not have this, please discuss with Professor Duchi.

Course communication, questions

• The course staff email address is stats116-spr2122-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 Ed this quarter for answering questions, finding collaborators, and other course-related things. You should be able to sign up at ed Stats 116

• 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 (.5 weeks)

• Axioms of probability (1 week)

• Independence and conditional probability (1 week)

• Random variables (2 weeks)

• Continuous random variables and distributions (2 weeks)

• Laws of large numbers and the central limit theorem (2 weeks)

• Concentration inequalities (1 week)

Grading

Your grade will be determined by weekly problem sets (55%), an in-class midterm (15%), and an in-person final exam (30%). 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 Wednesday, June 8, 12:15 – 15:15.

There will be weekly homework assignments throughout the course, which will count for 55% 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.