STAT 425   Probability Theory   Fall 2004

Instructor: Allan Rossman
Class Times: MTuWTh 8:10-9:00   room 022-315
Office: Faculty Office Building East 25-102
Phone: 756-2861 (6-2861 on campus)
Email: arossman@calpoly.edu
Office Hours: Mondays 3:10-4:00, Tuesdays 12:10-1:00, Wednesdays 4:10-5:00, Thursdays 9:10-10:00, and by appointment and by chance
Text: Probability and Statistics (3rd edition), by Morris H. DeGroot and Mark J. Schervish

Course Webpage: http://statweb.calpoly.edu/rossman/stat425/
Course Listserv: stat425@calpoly.edu

Overview: Much of statistics builds on a foundation of probability theory.  Probability is the mathematical study of randomness and uncertainty. It can be considered a great intellectual achievement, because while a random process is unpredictable in the short term, we can make very accurate predictions about the pattern of variation from that process in the long term. We will pay particular attention to those aspects of probability theory that have application to statistics.

Goals: By the conclusion of the course, I hope that you have improved your ability to:

  • understand probability concepts
  • derive and prove probability results
  • apply probability methods to solve problems
  • use the computer to investigate random phenomena, and
  • communicate your knowledge of probability effectively

Class Policies: I expect class meetings to be fairly informal.  During a typical class period I will present new material, but at times I will ask you to work on problems and present solutions.  I strongly encourage you to bring questions to class and to interrupt me with questions as they occur to you.

Please come prepared to participate in class.  By this I primarily mean two things:

  • Please read relevant sections of the text before coming to class.  Read carefully, and come to class with questions on what you do not understand.
  • Please be willing (or, even better, eager!) to ask questions and contribute answers and work on problems (when I ask you to) during class.

I also expect you to devote 8-12 hours per week, outside of class time, to your work for this course.  I anticipate that this work will include:

  • reading the textbook
  • reviewing and organizing your class notes
  • formulating questions to ask in class and office hours
  • working on homework assignments
  • working on investigation assignments
  • studying for exams

Naturally, you can and should expect me to prepare for class and to devote substantial time to the course outside of class as well.

Grading Policies: Your course grade will be determined by the following components, with relative weights as indicated:

  • homework assignments (15%)
  • investigation assignments (15%)
  • two midterm exams (20% each)
  • comprehensive final exam (30%)

Homework Assignments: Regular homework assignments will be made, roughly weekly.  About half of the problems will be from the book and half that I write myself.  Be aware that answers to odd-numbered problems appear in the back of the book, but you will be graded on your solutions and explanations, not simply on final answers.  You are encouraged to discuss homework problems with each other, but your solutions must be written up individually in your own words. You are encouraged to ask questions about these problems (ahead of time!) inside and outside of class. These assignments are due by 4pm on the indicated day.  You may have up to a 24-hour extension on the due date for one of these assignments; other than that, late assignments will not be accepted except for very compelling circumstances.

Investigation Assignments: Regular "investigation" assignments will also be made.  These are more open-ended and require more writing than homework problems.  They also typically involve computer work, usually using Minitab.  You may work with one other person on these investigations, handing in one report with both of your names. Word-processed reports of investigations are preferred to hand-written ones, and computer output should be integrated into your report.  These assignments are due by 4pm on the indicated day.  You may have up to a 24-hour extension on the due date for one of these assignments; other than that, late assignments will not be accepted except for very compelling circumstances.

The purposes of these homework and investigation assignments are:

  • to give you the practice with proof and problem-solving techniques in order to learn, understand, and apply the course material,
  • to provide you with feedback regarding your understanding of the material,
  • to further your discovery and exploration of course material, and
  • to prepare you for the kinds of questions that will be on the exams.

Exams: You will received detailed guidelines regarding the exams a week or so in advance.  They will be open-book and open-notes, and they will involve both in-class and take-home components. You may make up an exam only with a written medical excuse.

Advice: With apologies to David Letterman, I offer the following "Top Ten" suggestions to improve your learning in this course:

  • Come to class.
  • Participate in class.
  • Invest time outside of class.
  • Read carefully.
  • Ask questions.
  • Use office hours.
  • Start assignments early.
  • Work together.
  • Write well.
  • Think!

A common theme emerges from this list: You are responsible for your own learning.  As your instructor, I view my role as providing you with contexts and opportunities which facilitate the learning process. Please call on me to help you with this learning in whatever ways I can.

Tentative Schedule: The following is always subject to change but should give you a sense for what topics we will cover and when:

Week

Dates

Topics

Sections from Text

1

Sept 20-23

Set Theory, Basics of Probability, Counting Methods

1.4, 1.5, 1.6, 1.7

2

Sept 27-30

Combinatorial Methods

1.8. 1.9, 1.10, 1.11

3

Oct 4-7

Conditional Probability, Independence

2.1, 2.2

4

Oct 11-14

Bayes' Theorem, Exam

2.3

5

Oct 18-21

Markov Chains, Gambler's Ruin

2.4, 2.5

6

Oct 25-28

Discrete and Continuous Random Variables, Distribution Functions

3.1, 3.2, 3.3

7

Nov 1-4

Bivariate, Marginal, Conditional, and Multivariate Distributions

3.4, 3.5, 3.6, 3.7

8

Nov 8-10

Functions of Random Variables, Exam

3.8, 3.9

9

Nov 15-18

Expectation, Properties, Variance

4.1, 4.2, 4.3

10

Nov 22-23

Moments, Measures of Center

4.4, 4.5

11

Nov 29 - Dec 2

Covariance, Conditional Expectation

4.6, 4.7

 

Dec 10, 7:10-10:00am

Final Exam

 

Disclaimer: I am not always as organized as this lengthy syllabus might suggest. All of these details are subject to change as the course develops. I welcome and value your input.