LAB 01
Conditional Probability
Monty Hall
Choose among three, four, or five doors, watch the host reveal a goat, and decide whether to stay or switch. Compare the two strategies over repeated rounds.
Open labSTAT2002: Probability Theory and Mathematical Statistics
Course overview
This course introduces probability theory and mathematical statistics, covering events, conditional probability, independence, random variables and joint distributions, expectation and variance, and limit theorems. Building on these foundations, it develops statistical inference through sampling distributions, point and interval estimation, large-sample theory, bootstrap methods, and hypothesis testing, including p-values, likelihood-ratio tests, and goodness-of-fit tests.
Course materials
Course materials will be continuously updated throughout the course.
Syllabus
Lecture 1: Events and Their Probabilities (1)
Lecture 2: Events and Their Probabilities (2)
Lecture 3: Random Variables and Their Distributions (1)
Lecture 4: Random Variables and Their Distributions (2)
Lecture 5: Multivariate Random Variables and Their Distributions
Lecture 6: Numerical Characteristics of Random Variables and Limit Theorems
Lecture 7: Basic Statistical Concepts and Sampling Distributions
Labs
LAB 02
Entropy
Entropy and Distributions
Scatter points inside a unit disk. Adjust the variance and center of a truncated normal distribution, and compare its entropy with a uniform distribution.
Open lab
LAB 03
Limit Theorems
Law of Large Numbers and Central Limit Theorem
Adjust the number of coin tosses and the probability of heads. Compare concentration of sample means with the shape of their standardized distribution.
Open labCourse schedule
2026 Fall · Fridays 09:45–12:10 · Room 3A111
| Week | Date | Planned topics | Textbook / sections | Assignment |
|---|---|---|---|---|
| 1 | Sep 4 | A brief history of probability; random experiments, sample spaces, and events; definition and properties of probability | 1.1–1.3 | Assignment 1 |
| 2 | Sep 11 | Conditional probability; the law of total probability; Bayes’ formula; independence | 1.4–1.5 | Assignment 2 |
| 3 | Sep 18 | Random variables; discrete random variables and their distributions | 2.1–2.2 | Assignment 3 |
| 4 |
Sep 20 Sunday; rescheduled from Sep 25 |
Continuous random variables and their distributions; distributions of functions of random variables | 2.3–2.4 | Assignment 4 |
| 5 | Oct 2 | No class — National Day holiday | ||
| 6 | Oct 9 | Random vectors; marginal distributions | 3.1–3.2 | Assignment 5 |
| 7 | Oct 16 | Conditional distributions; mutual independence; distributions of functions of random vectors | 3.3–3.5 | Assignment 6 |
| 8 | Oct 23 | Expectation, median, variance, moments, and entropy; the law of large numbers and the central limit theorem | 4.1–4.4 | Assignment 7 |
| 9 | Oct 30 | No class — Sports Day | ||
| 10 | Nov 6 | A brief history of statistics; basic concepts; populations, samples, and sampling distributions | 5.1–5.3 | |
| 11 | Nov 13 | Point estimation; the method of moments and maximum likelihood estimation | 6.1–6.3 | |
| 12 | Nov 20 | Criteria for evaluating estimators; large-sample theory of point estimation | 6.4–6.5 | |
| 13 | Nov 27 | Interval estimation; the pivotal quantity method | 7.1–7.2 | |
| 14 | Dec 4 | Large-sample methods; bootstrap confidence intervals; confidence limits | 7.3–7.5 | |
| 15 | Dec 11 | Hypothesis testing; tests for the mean and variance of a single normal population | 8.1; 8.2.1 | |
| 16 | Dec 18 | Comparing means and variances of two normal populations; paired-sample tests for means | 8.2.2–8.2.3 | |
| 17 | Dec 25 | Tests for a proportion; likelihood ratio tests; p-values; goodness-of-fit tests | 8.3–8.5; 9.1 | |
| 18 | Jan 1, 2027 | No class — New Year’s Day holiday |