**Course Announcement****Time:**Monday, Wednesday, Friday at 09:00 - 09:50 a.m.

**Location:**Lincoln Hall 312 (707 S Morgan St, Chicago, IL 60607)**Instructor:**Jie Yang

**Office:**SEO 513

**Phone:**(312) 413-3748

**E-Mail:**jyang06 AT uic DOT edu

**Office Hours:**Monday, Wednesday, Friday at 10:00 a.m. - 11:00 a.m. at UIC Zoom**Textbook:**R. V. Hogg, J. W. McKean, A. T. Craig,*Introduction to Mathematical Statistics*, 8th edition, 2019

**Reference Books:**Robert V. Hogg, Elliot A. Tanis, Dale Zimmerman,*Probability and Statistical Inference*, 9th Edition, 2015.

**Content:**Probability spaces, random variables and their distributions, conditional distribution and stochastic independence, special distributions, sampling distributions, limit theorems

**Prerequisite:**Grade of C or better in MATH 210**Homework:**Turn in every Wednesday before class via UIC Blackboard; half of the grade counts for completeness; half of the grade counts for correctness of one selected problem

**Exams:**This course will require students to be on campus for in-person exams on September 28th and November 9th, Wednesday, 9:00 AM - 9:50 AM.

**Project:**Students are required to work by themselves or in groups on course projects and submit their final reports before December 2nd, 2022, Friday, 9:00am. 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*.

**Course Syllabus**

**WEEK****SECTIONS****BRIEF DESCRIPTION**08/22 - 08/26 1.1; 1.2; 1.3 Introduction; Set Theory; Probability Set Function 08/29 - 09/02 1.3; 1.4; 1.4 Probability Set Function; Conditional Probability and Independence 09/05 - 09/09 Holiday; 1.5; 1.5 Random Variables 09/12 - 09/16 1.6; 1.7; 1.8 Discrete Random Variables; Continuous Random Variables; Expectation of a Random Variable 09/19 - 09/23 1.9; 1.10; 2.1 Special Expectations; Important Inequalities; Distributions of Two Random Variables 09/26 - 09/30 Review; **Exam-I**; 2.1Distributions of Two Random Variables 10/03 - 10/07 2.2; 2.2; 2.3 Transformation: Bivariate Random Variables; Conditional Distributions and Expectations 10/10 - 10/14 2.3; 2.4; 2.5 Conditional Distributions and Expectations; Independent Random Variables; Correlation Coefficient 10/17 - 10/21 2.6; 2.7; 2.7 Extension to Several Random Variables; Transformations: Random Vectors 10/24 - 10/28 2.8; 3.1; 3.2 Linear Combinations of Random Variables; Binomial and Related Distributions; Poisson Distribution 10/31 - 11/04 3.3; 3.4; 3.5 Gamma, Chi-Squared and Beta Distributions; Normal Distribution; Multivariate Normal Distribution 11/07 - 11/11 Review; **Exam-II**; 3.6*t*and*F*-Distributions11/14 - 11/18 3.7; 5.1; 5.2 Mixture Distributions; Convergence in Probability; Convergence in Distribution 11/21 - 11/25 5.2; 5.2; Holiday Convergence in Distribution 11/28 - 12/02 5.3; 5.3; 5.3 Central Limit Theorem

**Homework**- Homework #1, due 08/31/2022

- Homework #2, due 09/07/2022

- Homework #3, due 09/14/2022

- Homework #4, due 09/21/2022

- Homework #5, due 09/26/2022

- Homework #6, due 10/12/2022

- Homework #7, due 10/19/2022

- Homework #8, due 10/26/2022

- Homework #9, due 11/02/2022

- Homework #10, due 11/07/2022

- Homework #11, due 11/23/2022

- Homework #12, due 11/30/2022

- Homework #1, due 08/31/2022
**Handouts**- Mathematical Symbols
- Derivatives, Integrals and Series
- Power Series
- Table I: Poisson Distribution
- Table III: Normal Distribution

**Using R**- Download
**R**for Free -- the most popular software used by statisticians

- Learn R in 15 Minutes

- Use R to Compute Numerical Integrals

- RStudio -- a convenient set of integrated tools for R, including programming, plotting, and workspace management

- Downloadable Books on R:
*An Introduction to R*, by William N. Venables, David M. Smith and the R Development Core Team

*Using R for Data Analysis and Graphics - Introduction, Code and Commentary*, by John H. Maindonald

**More R Books in Different Languages ...**

- Download
**Relevant Course Materials**- Textbook Web Page -- including Errata page and R code

- Bruce K. Driver,
*Math 280 Probability Theory Lecture Notes*, 2018-2019 -- good for readers who want more relevant readings

- Flip a Coin Online -- so many different kinds of coins, for §1.1

- Basic Mathematical Symbols -- symbols commonly used in mathematics

- Barber's Paradox -- a famous counterexample in the history of set theory, for §1.2

- Russell's Paradox -- another famous counterexample in the history of set theory, for §1.2

- Edwards' Venn Diagrams -- a nice construction to higher numbers of sets,
for §1.2

- Cantor Function -- a mysterious function which grows considerably virtually without changing, for §1.5

- Textbook Web Page -- including Errata page and R code
**COVID-19 Impacts on Instruction**- UIC fall COVID-19 guidance -- COVID-19 vaccination required, Masks required, COVID-19 saliva testing, etc.

- Lecture Recording Privacy FAQ

We will be recording the class sessions, or portions of the class, for students who are unable to attend synchronously. The recording feature for others is disabled so that no one else will be able to record this session through Zoom, Blackboard Collaborate, Webex, or Echo360. Recording by other means is not permitted. The recorded class sessions will be posted on our Blackboard class website unless otherwise notified.

If you have privacy concerns and do not wish to appear in the recording, turn OFF your video and notify me in writing (via email) prior to the next class session. If you prefer to use a pseudonym instead of your name, please let me know what name you will be using, so that I can identify you during the class session. If you would like to ask a question, you may do so privately through the chat feature by addressing your question to me or your TA only (and not to “everyone”), or you may contact me or your TA by another private method, which we will agree upon in advance of class. If you have questions or concerns about this video recording policy, please contact me before the end of the first week of class.

- UIC fall COVID-19 guidance -- COVID-19 vaccination required, Masks required, COVID-19 saliva testing, etc.
## Disability Accommodations Statement

UIC is committed to full inclusion and participation of people with disabilities in all aspects of university life. Students who face or anticipate disability-related barriers while at UIC should connect with the Disability Resource Center (DRC) at drc.uic.edu, drc@uic.edu, or at (312) 413-2183 to create a plan for reasonable accommodations. In order to receive accommodations, students must disclose disability to the DRC, complete an interactive registration process with the DRC, and provide their course instructor with a Letter of Accommodation (LOA). Course instructors in receipt of an LOA will work with the student and the DRC to implement approved accommodations.

UIC Home | Library | MSCS | Jie's Home