Stats 117: Introduction to Probability

John Duchi, Stanford University, Autumn 2026

As noted on the course information page, we will cover the following topics (time permitting):

  • 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)

Lectures and course schedule (at least as planned)

We strongly recommend completing the readings (and will assume you have completed the readings in Sun et al.'s The Art of Chance). We will list supplementary chapters in Ross's First Course in Probability by the name Ross, chapters in Blitzstein and Hwang's Introduction to Probability by BH. These are not required, but often give excellent alternative perspective.

We recommend taking notes on the slides we have prepared as a way to organize your thoughts and the material from the course. Mueller and Oppenheimer's study, The Pen is Mightier than the Keyboard, suggests that note-taking is more effective for learning and remembering material than either typing or just paying attention.

Lecture Date Topics Additional Reading Slides
1 Wed, 23 September Classical probability definitions BH 1.1 – 1.3 01
2 Fri, 25 September Counting BH 1.4 02
3 Mon, 28 September Definitions of probability BH 1.6 03
4 Wed, 30 September Properties of probability BH 1.6 04
5 Fri, 2 October Conditional probability BH 2.1–2.4 05
6 Mon, 5 October Independence BH 2.4–2.5 06
7 Wed, 7 October Bayes Rule BH 2.3, 2.7–2.8 07
8 Fri, 9 October Random variables BH 3.1–3.3 08
9 Mon, 12 October Expected value BH 4.1–4.2 09
10 Wed, 14 October Transformations BH 3.7 10
11 Fri, 16 October Unconscious statisticians and variance BH 4.2–4.6 11
12 Mon, 19 October Named distributions BH 3.3–3.6 12
13 Wed, 21 October Joint distributions BH 7–7.1.1 13
14 Fri, 23 October Multivariate expectations BH 7.2 (ish) 14
15 Mon, 26 October Midterm Review exams
16 Wed, 28 October Covariance BH 7.3
17 Fri, 30 October Conditionals and marginals
18 Mon, 2 November Conditional expectation BH 9.1–9.2
19 Wed, 4 November Continuous random variables BH 5.1–5.2
20 Fri, 6 November Expected value of continuous RVs BH 5.1–5.2 19
21 Mon, 9 November Transformations of Continuous RVs BH 5.3, 8.1
22 Wed, 11 November LotUS and Variance of Continuous RVs BH 5.1, 6.1–6.2
23 Fri, 13 November Named distributions BH 5.4–5.6
24 Mon, 16 November Joint densities (Normals) (joint densities) BH 7.1
25 Wed, 18 November Joint expectations BH 7.2
26 Fri, 20 November Covariance BH 7.3
NA Mon, 23 November Thanksgiving week, no classes
NA Wed, 25 November Thanksgiving week, no classes
N/A Fri, 27 November Thanksgiving week, no classes
27 Mon, 30 November Conditionals and marginals BH 9.1–9.3
28 Wed, 2 December Conditional expectation BH 9.1–9.3
29 Fri, 4 December Review or backup