STA 130A - Mathematical Statistics: Brief Course, Fall 2026

Course Information

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

Teaching Assistant: Dongchan Kim (dockim [at] ucdavis [dot] edu)

Lectures: Mondays, Wednesdays and Fridays, 11:00 AM – 11:50 AM, Wellman Hall 226

Discussions (Labs) are run by TA

Office hours:

Syllabus: link

Canvas: link

Piazza: link

Textbooks: There are two required textbooks, whose digital copies will be available on Canvas in Reading List.

Dimitri Bertsekas and John Tsitsiklis. Introduction to Probability, 2nd edition (2008), [Athena Scientific].
John Rice. Mathematical Statistics and Data Analysis, 3rd edition (2007), [Cengage Learning / Brooks/Cole].

A tentative list of topics to be covered include:

Probability basics
- Sample space and probability laws
- Set theory basics
- Conditional probability, total probability, and Bayes’ rule
- 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 and conditional distributions; independence, 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
Estimation
- Sampling distributions; chi-square, (t), and (F) distributions
- Point estimators and their properties
- Method of moments and maximum likelihood estimation
- (time permitting) Fisher information, efficiency, and selected topics in sufficiency

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

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	Notes
Wed, Sep 23	Introduction	Lecture 1
Fri, Sep 25	Set theory and probabilistic models	Lecture 2	BT, Ch 1.1 & 1.2	Homework 1 posted; due Thu, October 1
Mon, Sep 28	Conditional probability and Bayes’ rule	Lecture 3	BT, Ch 1.3 & 1.4
Wed, Sep 30	Independence and counting principle	Lecture 4	BT, Ch 1.5 & 1.6
Fri, Oct 2	Counting & Discrete random variables	Lecture 5	BT, Ch 1.6, 2.1 & 2.2	Homework 2 posted; due Thu, October 8
Mon, Oct 5	Expectation, mean and variance	Lecture 6	BT, Ch 2.3 & 2.4
Wed, Oct 7	Joint, marginal, and conditional distributions	Lecture 7	BT, Ch 2.5 & 2.6
Fri, Oct 9	Conditional expectation and independence	Lecture 8	BT, Ch 2.6 & 2.7	Homework 3 posted; due Thu, October 15
Mon, Oct 12	Continuous random variables	Lecture 9	BT, Ch 3.1 & 3.2
Wed, Oct 14	Normal random variables	Lecture 10	BT, Ch 3.3
Fri, Oct 16					TA’s extra office hour (noon–1pm)
Mon, Oct 19	Midterm 1 (in class)
Wed, Oct 21
Fri, Oct 23
Mon, Oct 26
Wed, Oct 28
Fri, Oct 30
Mon, Nov 2
Wed, Nov 4
Fri, Nov 6
Mon, Nov 9	Midterm 2 (in class)
Wed, Nov 11	No class (Veterans Day Holiday)
Fri, Nov 13
Mon, Nov 16
Wed, Nov 18
Fri, Nov 20
Mon, Nov 23
Wed, Nov 25	No class (Thanksgiving Holiday)
Fri, Nov 27	No class (Thanksgiving Holiday)
Mon, Nov 30
Wed, Dec 2
Fri, Dec 4
Mon, Dec 7	Final exam (3:30–5:30 PM)