601-362: Introduction to Mathematical Statistics II, Spring 1999

Instructor:

Professor Eric Key

Office:

EMS E455 229-4600 ericskey@uwm.edu

Hours:

I am teaching another class MW 10:30 - 11:50. I am usually here until 3 every day, so please come by at your convenience and I will be happy to speak to you if I am not busy with something that cannot be interrupted.

Website:

You will be able to find additional information about the course as the semester progresses by going to

http://www.uwm.edu/$\sim$ericskey/361F98.html

or by going to the mathematics department homepage and following the obvious links.

Content:

This is the second half of a year long course in mathematical statistics. The word ``mathematical'' is to distinguish this from a course whose purpose would be to present a wide variety of statistical tests with little regard to their derivation or optimal properties. While this course, and its predessor, 601-361, will present many statistical tests, a fair amount of time will be devoted to explaining the origins of the tests, why they are better than others, and what their limitations might be. This yearlong course is the only course on campus which will prepare students for the actuarial exam in probability and statistics.

Since the language of statistics is probability, the first semester will devoted a fair amount of time to developing those areas of probability theory needed for studying statistics. Along the way statistics concepts will be introduced where appropriate. In fact, the first topic we will discussed was an elementary example of hypothesis testing.

If you want or need a one semester course which covers statistical methods I suggest that you enroll in Mathematical Statistics 601-467 Introductory Statistics for Physical Sciences and Engineering Students. 601-467 has the same prerequisites as 601-361.

Grades:

There will be weekly and sometimes twice weekly homework assignments. Performance on these assignments will determine 40% of your grade. You will be allowed one late homework assignment, which must be turned in no later than 3:00 PM on the last day of classes.

There will be two in-class tests, each of which will determine 10% of your grade. These tests will be in late Febraury and early April. Make-up exams will be scheduled at my convenience and at my discretion. Personal illness or illness in the family are valid excuses.

There will be a final exam at the regularly scheduled time. Consult the schedule of classes. The final exam will determine 40% of your grade.

Books:

There are two required textbooks:

• Basic Probability Theory by Robert Ash. This will be on two hour reserve in the library and available in the bookstore.
• Mathematical Statistics with Applications by Mendenhall, Wackerly and Scheaffer.

There will be assigned reading and problems from both texts. From time to time I will also hand out additional things for you to read and problems for you to solve.

Both books were used in 601-361 in the fall.

You will also need a calculus book, such as the book by Thomas and Finney. It would be helpful to have a book which covers elementary linear algebra, such as the text for 600-234 or 318-234.

Computing:

You will also find it helpful to know how to use MAPLE or some similar program, to have scientific calculator which will generate random numbers and calculate binomial coefficients, a deck of cards and some dice.

Philosophy:

I believe that the way to learn mathematics is to solve a lot of problems. For this reason there will be a lot of homework in this course. My past experience indicates that if I were to require students to solve the homework problems on their own a sizable number of students would not and would present the work of others as their own. For this reason there will be exams. As far as the working on the homework goes, I encourage you to try to solve the problems individually. If you cannot, and you get help from someone else (preferably me) I expect you to give credit to your sources of assistance. A short note, such as ``Professor Klosek showed me how to do this'' or ``Hanna Martel suggested that I try the following'' is sufficient.

If I determine that you have not done so, I will consider this to be plagiarism and deal with it according to the established university procedures.

I am told that many of you are taking this course in order to prepare to become actuaries. For this reason I am going to require you to memorize any formulae which you would have to know for the actuarial exams. I don't like to have students memorize things, but this seems to be unavoidable. For me, the best way to memorize formulae is to use them a lot. Hence the large amount of homework.

I hope that you will make full use of calculators, computers, etc on the homework assignments. Test problems will be sorts of things where a calculator or computer will either be useless or contrary to the point of the the question. For this reason, calculators will not be permitted on the exams.