Introduction to Probability

Course information

  • Quarter: Fall 2024
  • Lecture time: Mondays and Wednesdays 1:30-2:50pm
  • Lecture location: STLC 111
  • 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 a combination of in-person class meetings with the professor and sections with CAs. All assignments will be posted on Canvas. Announcements will also be made through the Canvas site, and any questions should be posted to Ed.

  • Lecture: Our class will meet on Mondays and Wednesdays from 1:30-2:50 PM in STLC 111.
  • Section: Each student will be assigned to one hour-long weekly section on Fridays (starting at 11am, 12pm, or 2pm). The section will consist of about one third of the students. A CA will guide the students through problems related to the week’s lecture and homework. The key to success in this class is doing practice problems, so we highly encourage you to attend. The sign-up form for sections will go out on the first day of class, and the deadline for filling out that form will be midnight on Wednesday night. We will let you know which section you are in by the weekend, and you will have your first section during Week 2.
  • Homework: You will submit your weekly homework assignments on Gradescope (linked to on Canvas). The deadline for each homework will be Thursdays at 12pm.

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.