Help @ARC

The ARC provides the following free services:
- Peer tutoring for a wide range of courses
- Exam reviews
- Supplement Instruction
- Workshops and Seminars
- Group study
- Computing and Printing
Location: Hermann Hall Building-First Floor (Northwest Corner) Room HH-112
Telephone: (312) 567-5216
Email: arc@iit.edu

Software help

JMP software is available to students at IIT labs on campus.

Download R, and to read about it, click on the link "What is R"?

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.
See also Prof. Yang's post on learning R in 15 minutes.

Help with typing math: TeX, etc.

You are encouraged to type your assignments. You can access LaTeX in the computer labs; more information and help can be found on this departmental page. Note: for Macs, I recommend TeXShop.
You might also consider using the what-you-see-is-what-you-get text editor TeXmacs; it makes it unnecessary for you to learn the LaTeX typesetting language while producing output of comparable quality. The program is freely downloadable, available for various platforms, able to import and export LaTeX files, and offers a plugin for Macaulay 2.

Math 476/563: Mathematical Statistics

Homework schedule

Homework assignments will be posted at least one week before the due date. It is your responsibility to check the course page on Piazza, which you can easily access directly or by logging into Blackboard, to obtain the assigned problems.

You are expected to start working on the homework sets early (not the day they are due or right before). It is extremely difficult to answer last-minute homework questions; particularly if you have not been participating in the Piazza discussion beforehand.

Help with writing up assignments

[Credit: the text in this paragraph is borrowed from Prof. Kaul.]
To improve your mathematical writing quickly, start by writing draft solutions to homework early. A day or two later after you have had time to forget what you wrote, read it. If it doesn’t make sense or convince you, rewrite it. Writing a solution requires saying what you mean and meaning what you say. Be intellectually honest. Intellectual dishonesty includes: 1) stating a “reason” without understanding its relevance. 2) Claiming a conclusion when you know you haven’t proved it. 3) Giving an example and claiming you have proved the statement for all instances.

Lecture schedule

You are expected to cover (at least at a high level) the assigned readings before coming to the lecture. This will help you follow the course and organize your notes. In the reading schedule below, "WMS" refers to Wackerly, Mendhall, Scheaffer, Mathematical Statistics with Applications.

Homework problem sets are naturally related to the material covered in the course; hence, homework numbers are listed next to the corresponding topic.

Dates..............  Tentative topics covered Assigned reading Related homework
January 12&14 Topic 1: What is statistical inference? Statistics and sampling distributions WMS: Sections 1.4, 7.1-7.4.
Homework 1 due 1/28.
January 21 Topic 1, continued.
Start of Topic 2: Estimation: point estimation basics. Bias. Goodness of a point estimator.
WMS: Sections 7.1-7.1
Start of 8.1-8.4. 		Homework 1 due 1/28.
January 26&28 Topic 2 (cont'd): Estimation: point estimation basics.
Topic 3: Estimation: Conidence intervals and sample size.
WMS: 8.1-8.4.
WMS: 8.5.
 Homework 2 due 2/4. Extended to 2/9!
February 2&4 Topic 3 (cont'd): Estimation: confidence intervals.
Some additional examples.
WMS: 8.5-8.9
Homework 3 due 2/11.
February 9&11 Topic 4 (cont'd): Properties of point estimators: efficincy, consistency, sufficiency. MVUEs. Rao-Blackwell. WMS: 9.1-9.5. Homework 4 due 2/18.
February 16&18 Topic 4 (cont'd): MVUEs. Rao-Blackwell.
Topic 5: Where do estimators come from? Methods of moments and maximum likelihood; Computing MLEs and examples.
WMS: 9.7, 9.8, and references given in the book.
Homework 5 due 2/25 (TBD)
February 23 QUIZ 1: In class, one page of notes allowed. Chapters 8 and 9. Homework sets 1 - 3.
February 23&25 Topic 5 (cont'd): Properties of Maximum likelihood estimators.
[invariance, consistency, efficiency, asymptotic normality.]
AND: review of Chapters 8 and 9.
Topic 6: Introduction to hypethesis testing:
Elements of a statistical test; 		WMS: 10.1-10.2
Homework 6 due 3/4
March 2&4 Topic 6 (cont'd) Common large-sample tests. Calculating Type II Error probabilities and finding sample size for Z tests
WMS: 10.3-10.5.
 Homework 7 due 3/25
MARCH 11th MIDTERM EXAM: In class, one page of notes allowed. Chapters 7, 8 and 9. Homework sets 1 - 5.
March 9&11 Topic 7: p values.
Small sample tests. (Hypothesis testing for variances - time permitting.) 		WMS: 10.6, 10.7, 10.8 (and 10.9, time permitting)
Homework 7 due 3/25
March 16-20 spring break Catch up on reading!
March 23&25 Topic 7, continued: Small sample tests, and hypothesis testing for variances.
Topic 8: Power of tests, Neyman-Pearson, Likelihood ratio tests.
 WMS: 10.9, 10.10, 10.11, 10.12.
Homework 8 due 4/1 (note: problem 4 postponed to hw9)
March 30 & April 1 Topic 8, continued: Likelihood ratio tests.
WMS: 10.12.
Homework 9 due 4/8
(extended to 4/10 if needed)
April 6&8 Topic 8, continued: likelihood rati tests.
Topic 9: Analysis of categorical data - an introduction.
WMS: 14.1-14.4. Homework 10 due 4/15
April 13&15 Finished chapter 14, including Fisher's exact test (exact p-value computation), chi-square test of independence in two-way contingency tables. WMS: 14.1-14.14
April 20&22 Topic 10: linear models.
Linear statistical models, method of least squares, properites of LS estimators (simple linear regression). 		WMS: 11.1-11.4 HW 11,last homework set of the semester, due 4/29.