STATS 100A - Introduction to Probability
Summer Session A 2026
Probability is the mathematics of uncertainty and the foundation of statistics, machine learning, and data science. This course covers probability spaces, conditioning and Bayes' rule, random variables, discrete and continuous distributions, joint distributions, covariance and correlation, conditional expectation, the law of large numbers, and the central limit theorem.
The course is organized around a few recurring themes: events as indicator functions, distributions as the central objects, named distributions arising from mechanisms or limits, the joint distribution as the complete description of a random system, and concentration as the reason statistical estimation works.
General info
- Meetings: MW 2:00-3:50pm, June 22-July 31, 2026.
- Format: Online, Summer Session A (Zoom meeting link).
- Instructor: Arash A. Amini.
- Office hours: TBA.
- TA: Ethan Young.
- Discussion section: MW 4:00-4:50pm, online.
- Announcements: Campuswire (Use code 5302).
- Homework Submission: Gradescope (code: 2DXY3N), one PDF per weekly assignment.
- Midterm: Monday, July 13, 2026, in class, covering Lectures 1-6.
- Final exam: Cumulative, official Summer Sessions slot TBA.
- Prerequisites: Mathematics 32B and Mathematics 33A (linear algebra).
Resources
- Homework, slides, notes, and other course materials will be posted in the course Box folder.
- Lecture videos: Summer 2026 YouTube playlist.
Textbook
- Blitzstein and Hwang, Introduction to Probability, 2nd ed. Free online at probabilitybook.net.
- The Harvard Stat 110 lecture videos are a useful supplement at the summer pace.
Assessment
| Component | Weight | Notes |
|---|---|---|
| Homework | 10% | Six weekly sets, lowest dropped; written problems plus a short Python simulation component in one PDF |
| Midterm | 40% | Monday, July 13; covers Lectures 1-6 |
| Final exam | 50% | Cumulative, weighted toward the second half |
Homework includes Python simulation problems. You can use Google Colab to run the starter notebooks.
Tentative syllabus
| Lec | Date | Topic | Reading | Due |
|---|---|---|---|---|
| 1 | Jun 22 | What is probability? Spaces, events, counting | Ch. 1 | |
| 2 | Jun 24 | Conditioning, Bayes' rule, independence | Ch. 2 | |
| 3 | Jun 29 | Random variables and discrete distributions | Ch. 3 | HW 1 |
| 4 | Jul 1 | Expectation, the indicator method, the Poisson limit | Ch. 4 | |
| 5 | Jul 6 | Continuous random variables; universality of the uniform | Ch. 5 | HW 2 |
| 6 | Jul 8 | Moments and moment generating functions; midterm synthesis | Ch. 6 | |
| MT | Jul 13 | Midterm; joint distributions I | Ch. 7.1 | HW 3 |
| 8 | Jul 15 | Joint distributions II: covariance and correlation | Ch. 7.2-7.3 | |
| 9 | Jul 20 | Conditional expectation and prediction | Ch. 9 | HW 4 |
| 10 | Jul 22 | Concentration: the law of large numbers, Monte Carlo | Ch. 10.1-10.2 | |
| 11 | Jul 27 | The central limit theorem; inference, both ways | Ch. 10.3 | HW 5 |
| 12 | Jul 29 | Synthesis, capstone, and final review |
HW 6 is a short set on the central limit theorem.
Policies
- Late homework submitted up to 24 hours late receives 75% credit. Beyond that, it receives the dropped-lowest treatment.
- Collaboration on homework is encouraged, but submitted writeups and code must be your own.
- AI tools may be used, but try the problems yourself as much as possible. You will not have access to AI tools during exams.
- Exams are closed book and device-free. One double-sided handwritten note sheet is allowed for both exams.