STA 130A - Mathematical Statistics: Brief Course, Fall 2026
Instructor: Dogyoon Song (dgsong [at] ucdavis [dot] edu)
Teaching Assistant: TBA
Lectures: Mondays, Wednesdays and Fridays, 11:00 AM – 11:50 AM, Wellman Hall 226
- This is an in-person only class, and lectures will not be recorded.
Discussions (Labs) are run by TA
- Section B01: Tuesdays, 11:00 AM–11:50 AM, Hart Hall 1130
- Section B02: Tuesdays, 12:10 PM–1:00 PM, Olson Hall 147
Office hours:
- Dogyoon Song (Instructor): TBA
Syllabus: TBA
Canvas: TBA
Piazza: TBA
Textbooks:
There are two required textbooks, whose digital copy will be available on Canvas in Reading List.
- Dimitri Bertsekas and John Tsitsiklis. Introduction to Probability, 2nd edition (2012), [Athena Scientific].
- John Rice. Mathematical Statistics and Data Analysis, 3rd edition (2007), [Cengage Learning / Brooks/Cole].
Topics
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
Course Structure and Evaluation
The students’ performance in this course will be evaluated based on the following:
| Lecture Day |
Topics |
Slides |
Additional references |
HW |
Notes |
| Wed, Sep 22 |
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| Fri, Sep 24 |
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| Mon, Sep 28 |
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| Wed, Sep 30 |
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| Fri, Oct 2 |
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| Mon, Oct 5 |
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| Wed, Oct 7 |
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| Fri, Oct 9 |
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| Mon, Oct 12 |
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| Wed, Oct 14 |
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| Fri, Oct 16 |
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| Mon, Oct 19 |
Midterm 1 (in class) |
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| Wed, Oct 21 |
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| Fri, Oct 23 |
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| Mon, Oct 26 |
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| Wed, Oct 28 |
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| Fri, Oct 30 |
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| Mon, Nov 2 |
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| Wed, Nov 4 |
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| Fri, Nov 6 |
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| Mon, Nov 9 |
Midterm 2 (in class) |
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| Wed, Nov 11 |
No class (Veterans Day Holiday) |
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| Fri, Nov 13 |
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| Mon, Nov 16 |
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| Wed, Nov 18 |
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| Fri, Nov 20 |
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| Mon, Nov 23 |
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| Wed, Nov 25 |
No class (Thanksgiving Holiday) |
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| Fri, Nov 27 |
No class (Thanksgiving Holiday) |
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| Mon, Nov 30 |
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| Wed, Dec 2 |
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| Fri, Dec 4 |
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| Mon, Dec 7 |
Final exam (3:30–5:30 PM) |
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