Stats 117: Introduction to Probability

John Duchi, Stanford University, Spring 2022

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.

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