MA 585-01, Spring 2012
Class Schedule
- Monday, Wednesday 3:55 - 5:15
- 218 Shelby Center
Course Description and Goals
MA 585 is a beginning graduate-level course in probability. Topics include
- Probability spaces: random variables, conditional probability, independence, modes of convergence, measure theory
- Probability distributions: discrete and continuous distributions, joint and marginal distributions, transformations of random variables, distribution and quantile functions, convergence in distribution
- Expected value: properties of general expected value, variance, covariance and correlation, generating functions, conditional expected value
- Special models and distributions: Bernoulli trials and the binomial and negative binomial distributions, the Poisson model and the Poisson and gamma distributions, finite sampling models and the hypergeometric distribution, the normal distribution
- Fundamental theorems: the law of large numbers, the central limit theorem
Goals of the course include
- A deep understanding of the special language, notation, and point of view of probability.
- The ability to solve computational problems in probability.
- The ability to construct proofs of basic theorems in probability.
- The ability to use special models, including Bernoulli trials, finite sampling models, and the Poisson model
- A good understanding the fundamental theorems of probability, including the law of large numbers and the central limit theorem
- An improved ability to read, write, speak, and think in mathematical terms.
This course also prepares students for further study, including MA 685 Stochastic Processes, and ST 687 Theory of Statistics. Credit hours: 3
Prerequisites
Instructor Information
Office Hours
- Monday-Thursday 2:15 - 3:45
Course Materials
To use the web-based course material, you will need a modern browser with good JavaScript support. The latest versions of Chrome, Firefox, and Safari are best. Mathematical expressions will display best if you have the STIX Fonts installed. Click on the links to install or update your browser.
If you are unable to access the materials in web form, the link below gives the printed material in PDF form.
References
- A Course in Probability, Neil Weiss, Pearson/Addison Wesley
- Probability and Random Processes, Geoffrey Grimmett and David Stirzaker, Oxford
- Introduction to Probability Models, Sheldon Ross, Academic Press
- Probability: Theory and Examples, Richard Durrett, Brooks/Cole
Grade Determination
- Quizzes and graded homework: 1/6
- Two Tests: 1/2
- Final Exam: 1/3
Final Exam
- Final Exam: Wednesday, May 2, 3:00 - 5:30
Grading Scale (%)
- 90-100
- 80-89
- 70-79
- 60-69
- 0-59
Policies
- Consult the Student Handbook for information about the grievance procedure, accommodations for students with disabilities, or academic misconduct.
If you have difficulties or complaints related to this course, your first action usually should be to discuss them with me. If such a discussion would be uncomfortable for you or fails to resolve your difficulties, you should contact Professor Li, Chair of the Department of Mathematics. Professor Li's office is 258B Shelby Center. His telephone number is 256.824.6470. If you still are unsatisfied, you should discuss the matter with the Dr. Daniel Rochowiak, Associate Dean of the College of Science. Dean Rochowiak's office and telephone number are MSB C206 and 256.824.6605.
Test and Quizzes
Quizzes
- Quiz 1
- Quiz 2
- Quiz 3
- Quiz 4
- Quiz 5
- Quiz 6
- Quiz 7
- Quiz 8
- Quiz 9
- Quiz 10
Tests
- Test 1
- Test 2
- Test 3
Assignments
Week 1
- Monday, January 9. Update your browser and install the fonts, if necessary, so that you can access the course materials. Read Section 1.1 and work the exercises.
- Wednesday, January 11. Read Section 0.1 and work problems 1, 12, 13, 21, 25, 26, 32, 33. Read Section 1.2 and work problems 15, 17, 18, 21, 23, 24, 27, 31.
Week 2
- Monday, January 16. Holiday, no class
- Wednesday, January 18. Read Section 0.2 and work problems 7, 8, 11, 12. Read Section 0.9 and work problems 1-5.
Week 3
- Monday, January 23. In Section 1.3, work problems 1-25, 29, 23-37. Read Section 1.7.
- Wednesday, January 25. Continue with Section 1.3. Work problems 38-61.
Week 4
- Monday, January 30. Read the basic theory in Section 1.4. Work problems 1-24.
- Wednesday, February 1. Continue with Section 1.4. Work problems 27, 30-43, 46-49.
Week 5
- Monday, February 6. Read the basic theory in Section 1.5. Work problems 1-20.
- Wednesday, February 8. Continue with Section 1.5. Work problems 21-34, 38-51.
Week 6
- Monday, February 13. Read Section 1.6 and work problems 1-29
- Wednesday, February 15. Read Section 1.7. Test 1 due next Monday.
Week 7
- Monday, February 20. Read Section 2.1. Work problems 1-58.
- Wednesday, February 22. Read Section 2.2. Work problems 1-43, 48-51.
Week 8
- Monday, February 27. Read Section 2.3 and work the problems.
- Wednesday, February 29. Read Section 2.4 and work the problems.
Week 9
- Monday, March 5. Read Section 2.5 and work the problems.
- Wednesday, March 7. Read Section 2.6 and work the problems.
Week 10
- Monday, March 12. Read Section 2.7 and work the problems.
- Wednesday, March 14. Read Section 2.8 and work the problems. Test 2 is due on March 28.
Week 11. Spring break
- Monday, March 19. No class
- Wednesday, March 21. No class
Week 12
- Monday, March 26. Continue with Section 2.8.
- Wednesday, March 28. Read Section 3.1 and work the problems.
Week 13
- Monday, April 2. Continue with Section 3.1.
- Wednesday, April 4. Read Section 3.2 and work the problems.
Week 14
- Monday, April 9. Continue with Section 3.2. Start Section 3.3.
- Wednesday, April 11. Continue with Section 3.3.
Week 15
- Monday, April 16. Read Section 3.5 and work the problems.
- Wednesday, April 18. Continue with Section 3.5.
Week 16
- Monday, April 23. Read Section 3.4. Test 3 is due Monday, April 30. Final Exam is Wednesday, May 2.