Time: Monday, Wednesday, Friday at 10:00 - 10:50 a.m.
Location (in person and on campus): Lecture Center Building A (805 S Morgan St, Chicago, IL 60607), Room A003
Instructor: Jie Yang
Office: SEO 513
Phone: (312) 413-3748
E-Mail: jyang06 AT uic DOT edu
Office Hours: Monday, Wednesday, Friday at 11:00 a.m. - 11:50 a.m. at UIC Zoom or by appointment
Textbook (required): R. V. Hogg, J. W. McKean, A. T. Craig,
Introduction to Mathematical Statistics, 8th edition, 2019.
Reference Books (optional):
Robert V. Hogg, Elliot A. Tanis, Dale Zimmerman,
Probability and Statistical Inference, 10th Edition, 2022.
Course Description: STAT 401. Introduction to Probability.
Probability spaces, random variables and their distributions, conditional distribution and stochastic independence, special distributions, sampling distributions, limit theorems.
Course Credits: 3 hours for undergraduates or 4 hours for graduate students.
Prerequisite: Grade of C or better in MATH 210.
Course Goals: Teach students core probability concepts, including random variables, probability distributions, and limit theorems, to build a strong foundation for mathematical statistics.
Learning Objectives: Understand set theory, probability set functions, conditional probability, and stochastic independence; analyze discrete and continuous random variables, their probability distributions, and transformations; compute expectations, variance, and correlation coefficients; and study special distributions, sampling distributions, and fundamental limit theorems.
Attendance/Participation Policy:
Students are expected to attend the lectures and participate in the discussions. Attendance will be counted at least six times during the course period and the students who present may receive half credit point each time and up to three extra credit points in total on the final grade at a 100-point scale. Students who actively participate in the discussion may receive half or one credit point each time and up to five credit points in total. If for any reason you could not present in class on time, please send me an email at your earliest convenience. If you need special accommodations due to disabilities, please contact the Disability Resource Center for a Letter of Accommodation (LOA).
Assignments, Due Dates, and Deadlines:
Homework will be assigned at a weekly basis;
turn in your homework every Friday before class via UIC Canvas;
half of the grade counts for completeness;
half of the grade counts for correctness of one selected problem.
Policy for Missed or Late Homework: Students may request up to three days' extension for each homework; late homework without request ahead of time or longer than three days will not be accepted; the lowest two homework scores will be dropped for final grade.
Exams: This course will require students to be on campus for in-person exams on September 30th (Wednesday) and November 11th (Wednesday), 10:00 AM - 10:50 AM.
Project: Students are required to work by themselves or in groups on course projects and submit their final reports before December 4th, 2026, Friday, 10:00am.
Each group should consist of at most three students. The projects may come from the optional problems assigned
by the instructor or be proposed by the students themselves upon the approval of the instructor.
Grading: Homework 20%, Two Exams 25% each, Project 30%.
Grading Scale: 90% A , 80% B , 70% C , 60% D.
Format of All Exams: Each exam is based on the homework and the examples discussed in class. The last class session before each exam is a review session. Please prepare any questions that you may have.
No makeup exam will be given without a valid excuse.
| WEEK | SECTIONS | BRIEF DESCRIPTION |
| 08/24 - 08/28 | 1.1; 1.2; 1.3 | Introduction; Set Theory; Probability Set Function |
| 08/31 - 09/04 | 1.3; 1.4; 1.4 | Probability Set Function; Conditional Probability and Independence |
| 09/07 - 09/11 | Holiday; 1.5; 1.5 | Random Variables |
| 09/14 - 09/18 | 1.6; 1.7; 1.8 | Discrete Random Variables; Continuous Random Variables; Expectation of a Random Variable |
| 09/21 - 09/25 | 1.9; 1.10; 2.1 | Special Expectations; Important Inequalities; Distributions of Two Random Variables |
| 09/28 - 10/02 | Review; Exam-I; 2.1 | Distributions of Two Random Variables |
| 10/05 - 10/09 | 2.2; 2.2; 2.3 | Transformation: Bivariate Random Variables; Conditional Distributions and Expectations |
| 10/12 - 10/16 | 2.3; 2.4; 2.5 | Conditional Distributions and Expectations; Independent Random Variables; Correlation Coefficient |
| 10/19 - 10/23 | 2.6; 2.7; 2.7 | Extension to Several Random Variables; Transformations: Random Vectors |
| 10/26 - 10/30 | 2.8; 3.1; 3.2 | Linear Combinations of Random Variables; Binomial and Related Distributions; Poisson Distribution |
| 11/02 - 11/06 | 3.3; 3.4; 3.5 | Gamma, Chi-Squared and Beta Distributions; Normal Distribution; Multivariate Normal Distribution |
| 11/09 - 11/13 | Review; Exam-II; 3.6 | t and F-Distributions |
| 11/16 - 11/20 | 3.7; 5.1; 5.2 | Mixture Distributions; Convergence in Probability; Convergence in Distribution |
| 11/23 - 11/27 | 5.2; Holiday; Holiday | Convergence in Distribution |
| 11/30 - 12/04 | 5.3; 5.3; 5.3 | Central Limit Theorem |