STA 131A - Introduction to Probability Theory, Spring 2026

Course Information

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

Teaching Assistant: TBA

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: Wednesdays, 5:30 PM - 6:30 PM, or by appointment (MSB 4220)
• TA: TBA

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
  • Conditional probability and independence
  • Counting and basic combinatorics
• Discrete random variables
  • Probability mass functions (PMFs)
  • Expectation, variance and moments
  • Joint PMFs
  • Conditioning and independence
• General random variables
  • Probability density functions (PDFs) and cumulative distribution functions (CDFs)
  • Some exemplar random variables
  • Joint PDFs
  • Conditioning and independence (revisited)
• 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.