STA 131A - Introduction to Probability Theory, Spring 2026

Course Information

Instructor: Dogyoon Song (dgsong [at] ucdavis [dot] edu)

Teaching Assistant: Wonjun Seo (wseo [at] ucdavis [dot] edu)

Lectures: Mondays, Wednesdays and Fridays, 10:00 AM – 10:50 AM, Wellman Hall 226

This is an in-person only class, and lectures will not be recorded.

Discussions (Labs) are run by TA

Section A01: Thursdays, 3:10 PM – 4:00 PM, Hart Hall 1130
Section A02: Thursdays, 4:10 PM – 5:00 PM, Wellman Hall 115

Office hours:

Dogyoon Song (Instructor): Wednesdays, 2:30 PM – 3:30 PM, or by appointment (MSB 4220)
Wonjun Seo (TA): Tuesdays, 3:00 PM – 5:00 PM (MSB 1117)

Syllabus: link

Canvas: link

Piazza: link

Textbooks: There is one required textbook, whose digital copy is available on Canvas in Reading List.

Dimitri Bertsekas and John Tsitsiklis. Introduction to Probability, 2nd edition (2012), [Athena Scientific].

Topics

A tentative list of topics to be covered include:

Probability basics
- Sample space and probability
- Set theory basics
- Counting and basic combinatorics
Discrete and continuous random variables
- Probability mass functions (PMFs), probability density functions (PDFs) and cumulative distribution functions (CDFs)
- Expectation, variance and moments
- Some exemplar random variables
- Joint distributions
- Conditioning and independence
Further topics on random variables
- Derived distributions
- Covariance and correlation
- (Laplace) transform and moment generating function
Limit theorems
- Markov and Chebyshev inequalities
- The (weak) law of large numbers
- The central limit theorem

Course Structure and Evaluation

The students’ performance in this course will be evaluated based on the following:

Homework: 40%
Midterms: 25%
Final exam: 35%
Participation: up to 3% extra

Tentative Class Schedule

Before the course begins, students should complete the “Homework 0” for self-assessment; this will not be collected or graded, and no solutions will be provided.

Lecture Day	Topics	Slides	Additional references	HW
Mon, Mar 30	Introduction	Lecture 1	BT, Ch 1.1 & 1.2	“HW 0”
Wed, Apr 1	Set theory and probabilistic models	Lecture 2	BT, Ch 1.1 & 1.2	Homework 1 posted; due Tue, April 7
Fri, Apr 3	Conditional probability and Bayes’ rule	Lecture 3	BT, Ch 1.3 & 1.4
Mon, Apr 6	Independence	Lecture 4	BT, Ch 1.5
Wed, Apr 8	Counting	Lecture 5	BT, Ch 1.6	Homework 2 posted; due Tue, April 14
Fri, Apr 10	Discrete random variables	Lecture 6	BT, Ch 2.1 & 2.2
Mon, Apr 13	Expectation, mean and variance	Lecture 7	BT, Ch 2.3 & 2.4
Wed, Apr 15	Expectation (cont’d) & Joint PMFs	Lecture 8	BT, Ch 2.5	Homework 3 posted; due Tue, April 21
Fri, Apr 17	Conditioning	Lecture 9	BT, Ch 2.6
Mon, Apr 20	Independence	Lecture 10	BT, Ch 2.7
Wed, Apr 22	Review for Midterm 1	Lecture 11
Fri, Apr 24	Midterm1 (in-class)	Solution
Mon, Apr 27	Continuous random variables	Lecture 12	BT, Ch 3.1
Wed, Apr 29	Cumulative distribution functions	Lecture 13	BT, Ch 3.2	Homework 4 posted; due Tue, May 5
Fri, May 1	Normal random variables	Lecture 14	BT, Ch 3.3
Mon, May 4	Joint PDFs of multiple random variables	Lecture 15	BT, Ch 3.4		Remote lecture; see Canvas announcement
Wed, May 6	Conditioniong continuous random variables	Lecture 16	BT, Ch 3.5	Homework 5 posted; due Tue, May 12
Fri, May 8	More topics on conditioniong	Lecture 17	BT, Ch 3.6 & 4.3
Mon, May 11	Derived distributions	Lecture 18	BT, Ch 4.1
Wed, May 13	Derived distributions (cont’d) & Review for Midterm 2	Lecture 19	BT, Ch 4.1
Fri, May 15	Midterm2 (in-class)	Solution
Mon, May 18	Covariance and conditional variance	Lecture 20	BT, Ch 4.2 & 4.3
Wed, May 20	Moment generating functions	Lecture 21	BT, Ch 4.3 & 4.4	Homework 6 posted; due Tue, May 26
Fri, May 22	Sums of independent random variables	Lecture 22	BT, Ch 4.4 & 4.5
Mon, May 25	Memorial day, no class
Wed, May 27	Markov and Chebyshev inequalities	Lecture 23	BT, Ch 5.1	Homework 7 posted; due Tue, June 2
Fri, May 29	The weak law of large numbers	Lecture 24	BT, Ch 5.2 & 5.3
Mon, Jun 1	The central limit theorem	Lecture 25	BT, Ch 5.4
Wed, Jun 3	Review for final exam & Conclusion	Lecture 26

Thu, Jun 11	Final exam (1:00 - 3:00 PM)	Solution

Practice exams and solutions: