Please note that the official course website is on Canvas (log in with CNetID), NOT here. This webpage is for those who are interested in STAT 24400 to get an idea of what the course is like.
STAT 24400 is the first quarter of a two-quarter systematic introduction to the principles and techniques of statistics, as well as to practical considerations in the analysis of data, with emphasis on the analysis of experimental data. This course covers tools from probability and the elements of statistical theory. Topics include the definitions of probability and random variables, binomial and other discrete probability distributions, normal and other continuous probability distributions, joint probability distributions and the transformation of random variables, principles of inference (including Bayesian inference), maximum likelihood estimation, hypothesis testing and confidence intervals, likelihood ratio tests, multinomial distributions, and chi-square tests. Examples are drawn from the social, physical, and biological sciences. The coverage of topics in probability is limited and brief, so students who have taken a course in probability find reinforcement rather than redundancy. Students who have already taken STAT 25100 have the option to take STAT 24410 (if offered) instead of STAT 24400. See www.stat.uchicago.edu/~yibi/IntroStat for help deciding between Stat 200, 220, 234, 244, and 24410.
Interested in being a Statistics major or minor? ask Yibi Huang yibih@uchicago.edu.
MATH 18400 w/ B or better or (Math 15250 and Math 15300 both B or better), or MATH 16300/16310/20250/20300/20310/ 20700 w/ C+ or better, or enrolled in MATH 16300/16310/18400/20250/20300/20310/20700 during preregistration
Mathematical Statistics and Data Analysis, by John Rice, 3rd edition
| Week/Date | Slides | Content | Textbook Coverage |
|---|---|---|---|
| Week 1 – June 10, 12 | L01 | Introduction to Probability: Sample Space, Events, Set Notations, Venn Diagram, Probability Measure; Counting Methods (Permutation, Combination) | Section 1.1-1.4 |
| Week 1 – June 12, 13 | L02 | Conditional Probability, Multiplication Law, Law of Total Probability, Bayes Rule, Independence | Section 1.5-1.6 |
| Week 1 – June 13Week 2, June 17 | L03 | Discrete Random Variables, Bernoulli, Binomial, Binomial, Geometric, Negative Binomial, Hypergeometric, Poisson distributions | Section 2.1 |
| Week 2 – June 19 | Juneteenth, No Class | - | |
| Week 2 – June 20Week 3 – June 24 | L04 | Continuous Random Variables (PDF, CDF), Functions of a Random Variable, Transform to Uniform; How to Generate a Random Variable From a Given CDF | Section 2.2-2.3 |
| Week 3 – June 24, 26 | L05 | Joint distribution, Marginal Distribution, Independent random variables | Section 3.1-3.4 |
| Week 3 – June 26, 27 | L06 | Conditional Distributions | Section 3.5 |
| Week 3 – June 27Week 4 – July 1 | L07 | Functions of 2+ Random Variables, Order Statistics | Section 3.6-3.7 |
| Week 4 – July 1 | L08 | Expected Value, Variance, SD | Section 4.1-4.2 |
| Week 4 – July 3 | L09 | Covariance & Correlation | Section 4.3 |
| Week 4 – July 4 | July 4th. No Class | - | |
| Week 5 – July 8 | Midterm Exam. No Class | - | |
| Week 5 – July 10, 11 | L10 | A Technique to Find Expected Value and Variance without Knowing the Distribution; Conditional Expectation & Variance, Tower Law for Expected Value and Variance | Section 4.4 |
| Week 5 – July 11Week 6 – July 15 | L11 | Moment Generating Functions | Section 4.5 |
| Week 6 – July 15, 17 | L12 | Limiting Distributions: Law of Large Numbers & Central Limit Theorem] | Chapter 6 |
| Week 6 – July 17, 18 | L13 | Chi-squared, t, and F-distributions; Sample Mean, Sample Variance, their Independence, and Distributions | Section 8.3-8.5 |
| Week 6 – July 18Week 7 – July 22 | L14 | Parameter Estimation, MSE, Sampling Distributions, Standard Error, Method of Moments; Maximum likelihood estimate | Section 8.3-8.5 |
| Week 7 – July 24 | L15 | Large Sample Theory of MLEs; Fisher Information; Cramer-Rao Lower Bound | Section 8.5, 8.7 |
| Week 7 – July 25 | L16 | Bayesian Approach to Parameter Estimation; Credible Intervals | Section 8.6 |
| Week 8 – July 29, 31 | L17 | Intro to Hypothesis Testing; Likelihood Ratio Tests | Section 9.2-9.4 |
| Week 8 – August 1 | L18 | P-value; Tests About Normal Distributions | |
| Week 9 – August 5 | L19 | Chi-Squared Tests for Multinomial Data | Section 9.5 |
| Week 9 – August 7 | -- | Summary & Review | - |
| Week 9 – August 8 | Final Exam. No Class | - |