**Course Announcement**

**Time:**Monday, Wednesday, Friday at 10:00 - 10:50 a.m.

**Location:**Taft Hall 117**Instructor:**Jie Yang, SEO 513

**Office Hours:**Monday, Wednesday, Friday at 12:00 - 13:00 p.m.**Teaching Assistant:**John Hardwick

**Office Hours:**Monday and Friday at 3:00 - 4:00 p.m., Math Learning Center (SEO 430)**Textbook:**R. V. Hogg, J. W. McKean, A. T. Craig,*Introduction to Mathematical Statistics*, 7th edition, 2012(recommended) or 6th edition, 2004

**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; half of the grade counts for completeness; half of the grade counts for correctness of one selected problem

**Midterms:**October 5th and November 16th, Friday, 10:00 a.m. - 10:50 a.m.

**Final Exam:**10:30-12:30 p.m. Friday, December 14

**Grading:**Homework 10%, midterms 25% each, final exam 40%

**Grading Scale:**93% A , 80% B , 65% C , 50% 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 (7th Edition)****BRIEF DESCRIPTION**08/27 - 08/31 1.1; 1.2; 1.3 Introduction; Set Theory; Probability Set Function 09/03 - 09/07 Holiday; 1.3; 1.4 Probability Set Function; Conditional Probability and Independence 09/10 - 09/14 1.4; 1.5; 1.5 Conditional Probability and Independence; Random Variables 09/17 - 09/21 1.6; 1.7; 1.8 Discrete Random Variables; Continuous Random Variables; Expectation of a Random Variable 09/24 - 09/28 1.9; 1.10; 2.1 Special Expectations; Important Inequalities; Distributions of Two Random Variables 10/01 - 10/05 2.1; Review; **Midterm-1**Distributions of Two Random Variables 10/08 - 10/12 2.2; 2.2; 2.3 Transformation: Bivariate Random Variables; Conditional Distributions and Expectations 10/15 - 10/19 2.3; 2.4; 2.5 Conditional Distributions and Expectations; Correlation Coefficient; Independent Random Variables 10/22 - 10/26 2.6; 2.7; 2.7 Extension to Several Random Variables; Transformations: Random Vectors 10/29 - 11/02 2.8; 3.1; 3.2 Linear Combinations of Random Variables; Binomial and Related Distributions; Poisson Distribution 11/05 - 11/09 3.3; 3.4; 3.5 Gamma, Chi-Squared and Beta Distributions; Normal Distribution; Multivariate Normal Distribution 11/12 - 11/16 3.6; Review; **Midterm-2***t*and*F*-Distributions11/19 - 11/23 3.7; 5.1; Holiday Mixture Distributions; Convergence in Probability 11/26 - 11/30 5.2; 5.2; 5.3 Convergence in Distribution; Central Limit Theorem 12/03 - 12/07 5.3; Review; Review Central Limit Theorem 12/10 - 12/14 **Final Exam**Final Exam

**Handouts**- Course Announcement
- Mathematical Symbols
- Derivatives, Integrals and Series
- Power Series
- Errata Sheet for Textbook (6th Edition)
- Table I: Poisson Distribution
- Table III: Normal Distribution

**Homework**- Homework #1, due 09/05/2012

- Homework #2, due 09/12/2012

- Homework #3, due 09/19/2012

- Homework #4, due 09/26/2012

- Homework #5, due 10/03/2012

- Homework #6, due 10/17/2012

- Homework #7, due 10/24/2012

- Homework #8, due 10/31/2012

- Homework #9, due 11/07/2012

- Homework #10, due 11/14/2012

- Homework #11, due 11/28/2012

- Homework #12, due 12/05/2012

- Homework #1, due 09/05/2012
**Using R**- Download
**R**for Free -- the most popular software used by statisticians

- Learn R in 15 Minutes

- Use R to Compute Numerical Integrals

- 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 Lecture Notes*, 2009-2010 -- good for readers who want more relevant readings (thank Yan Xing for recommendation)

- 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

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