MATH 481 Syllabus

## Math 481 Spring 2009 Mathematical Theory of Statistics

Lecturer: Prof. Roe Goodman

Office: Hill Center 428

Telephone Number: (732) 445-2390 ext. 3071

Office Hours: Tuesday & Thursday 2:00 - 3:00 PM (other times by appointment)

e-mail: goodman [at] math [dot] rutgers [dot] edu

Textbook: John E. Freund's Mathematical Statistics with Applications, Seventh Edition, by Miller and Miller,
Pearson/Prentice-Hall (ISBN 0-13-142706-7).

### Course Description:

This course develops the basic mathematical theory of statistics: sampling distributions, parameter estimation, confidence intervals, hypothesis testing, and linear regression and correlation. After a rapid presentation of chapters 5 and 6 of the text, the course covers chapters 8 and 10-14 in detail. This course has a theoretical focus; it does not emphasize statistical recipes or data analysis (you can learn these useful tools in several undergraduate courses in the statistics department). Rather, it teaches how to apply probability theory to obtain fundamental statistical methodologies. It serves as partial preparation for the actuarial exams in statistics.

Back to Math 481 main course page

Here is the
syllabus with homework assignments.
You will need some version of a graphing calculator to do some of the homework problems. There are also free web sites that host statistics calculators, such as Easy Calculation.com, and you can read more about most topics in the course in Wikipedia.
Important: Obtaining a numerical value for answers in the homework is important, but in your homework writeups you must justify the theoretical procedures in detail and show how you get the results.

### Prerequisites:

• Introductory Linear Algebra (01:640:250) and
• either
• Mathematical Theory of Probability (01:640:477)
or
• Multivariable Calculus (01:640:251) and
• Theory of Probability (01:960:381)

Credit restrictions: You cannot take this class for credit if you have already received credit for Theory of Statistics (01:960:382).

Note the that computer science course 198:206 is NOT an adequate prerequisite, because it does not cover continuous multivariate random variables and the limit theorems of probability (Law of Large Numbers, Central Limit Theorem), which are extensively used in 640:481. You can use Chapters 1-7 of the textbook (which is designed for a full year course) to review probability theory.

There will be two in-class exams during the semester and a final exam scheduled by the university scheduling office.
• Exam #1 (Thursday, February 26): 100 pts
• Exam #2 (Thursday, April 9): 100 pts
• Final Exam (Wednesday, May 13): 200 pts
• Collected homework: 100 pts

Makeup policy: It is assumed that students will take the examinations as scheduled. Makeup exams will only be given to students who have documented medical excuses.

The weekly homework assignments (generally 10 exercises from the text) should be handed in at the date indicated on the syllabus (generally on Tuesdays). Late homework is not accepted (no matter what the excuse). This is for the sake of all the students in the course, since detailed homework solutions will be posted when each assignment is returned. The only way to learn this subject and to do well on the exams is by doing all the homework problems every week of the term. This requires a considerable amount of time, since a total of 115 exercises are assigned. It can't be put off until the midterm and final exams approach.

Prof. Roe Goodman   (goodman at math dot rutgers dot edu) / Revised January 10, 2009