MA 385-01, Spring 2010

Course Description and Goals

This course is a calculus-based introduction to probability with special emphasis on the interplay between probability and statistics. Topics include

• descriptive statistics
• probability spaces
• discrete distributions (including the binomial, geometric, hypergeometric, and Poisson)
• continuous distributions (including the uniform, exponential, and normal)
• joint distributions
• mean, variance, and general expected value
• independence and correlation
• the law of large numbers
• the central limit theorem.

Goals of the course include

• A basic understanding of the special language, notation, and point of view of probability.
• A basic understanding of the interplay between probability and inferential statistics.
• The ability to solve standard computational problems in probability.
• The ability to recognize special models, including Bernoulli trials, finite sampling models, and the Poisson model
• An intuitive understanding the two fundamental theorems of probability: he law of large numbers and the central limit theorem
• An improve ability to read, write, speak, and think in mathematical terms.

This course also prepares students for further study, including MA 487, Introduction to Mathematical Statistics and MA 585, Probability. Credit hours: 3

Prerequisites

• MA 120, Calculus with Applications or MA 172, Calculus B
• One MA course at the 200-level or above; MA 201 recommended.

Instructor Information

• Instructor: Kyle Siegrist
• Office: 258K Shelby Center
• Voice: 824-6486
• Fax: 824-6173
• E-mail: siegrist@math.uah.edu

Office Hours

• Tuesday, 11:30 - 12:30, 2:30 - 3:30
• Wednesday, 2:00 - 4:00
• Thursday, 11:30 - 12:30, 2:30 - 3:30

Course Materials

• Class website (http://www.math.uah.edu/~siegrist/MA385/index.html). This site has the syllabus, assignments, tests and quizzes.
• Primary course material: Virtual Laboratories in Probability and Statistics (http://www.math.uah.edu/stat/)
• Reference text: Schaum's Outline in Probability and Statistics, Murray R Spiegel, John J. Schiller, R. Alu Srinivasan, published by McGraw Hill (2000), ISBN 0071350047

To use the web-based course material, Virtual Laboratories in Probability and Statistics, you will need the latest version of the Mozilla Firefox browser with the appropriate fonts installed. You will also need the latest version of Java plug-in and JavaScript enabled. Click on the links to install or update your browser and to install the plug-ins. The expository text is also given in PDF form, in case you are unable to use Firefox or if you want to print the text.

Course Outline

0. Foundations, Sections 1, 2, 7, 8
1. Probability Spaces, Sections 1, 2, 3, 4, 5
2. Distributions, Sections 1, 2, 4, 5, 6, 7
3. Expected Value, Sections 1, 2, 3, 4, 5

Class Schedule

• Tuesday, Thursday 3:55 - 5:15
• 207 Shelby Center

Grade Determination

• Quizzes and graded homework: 1/3
• Two class tests: 1/6 each
• Final Exam: 1/3

Exams

• Test 1: Thursday, February 25
• Test 2: Thursday, April 8
• Final Exam: Thursday, May 6, 3:00 - 5:30

Grading Scale (%)

1. 90-100
2. 80-89
3. 70-79
4. 60-69
6. 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 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 824-6605.

Tests and Quizzes

Tests

1. Test 1

Quizzes

1. Quiz 1
2. Quiz 2
3. Quiz 3
4. Quiz 4
5. Quiz 5
6. Quiz 6
7. Quiz 7
8. Quiz 8
9. Quiz 9
10. Quiz 10
11. Quiz 11

Assignments

Week 1

• Tuesday, January 12. Bookmark the syllabus. Install Firefox and the STIX fonts. Make sure that you can access the course materials and run the Java applets. Read Section 1.1 on Random Experiments, and work problems 1-16.
• Thrusday, January 14. No class; we will make up this class later.

Week 2

• Tuesday, January 19. Read Section 1.2. Work problems 18, 20, 21, 23, 27, 29, 32, 44, 45.
• Thursday, January 21. Read Section 0.7 and work problems 21, 22, 24-26, 29, 30, 32. Read Section 0.8 and work problems 25-27, 29-39.

Week 3

• Tuesday, January 26. Read Section 1.3 and work problems 29-32, 34, 37, 39, 42, 44, 47, 48.
• Thursday, January 28. Continue with Section 1.3. Work problems 49, 53, 55-58

Week 4

• Tuesday, February 2. Read Section 1.4 and work problems 7-10, 12, 15, 17, 18, 20, 22, 28-34, 36, 39-42.
• Thursday, February 4. Continue with the assignment in Section 1.4.

Week 5

• Tuesday, February 9. Read Section 1.5 and work problems 20-22, 26, 28, 29, 32-34, 39, 40, 42-45, 48-50, 51, 52.
• Thursday, February 11. Continue the assignment in Section 1.5.

Week 6

• Tuesday, February 16. Class canceled
• Thursday, Februrary 18. Class canceled

Week 7

• Tuesday, February 23. Study for Test 1 on Sections 0.7, 0.8, 1.1-1.5.
• Wednesday, February 24. Problem session, 2:30 - 3:45, 105 Shelby Center
• Thursday, February 25. Test 1. Read Section 2.1 and work problems 18, 20, 22, 24, 28, 29, 31, 33, 35, 39, 40, 44, 45, 46.

Week 8

• Tuesday, March 2. Continue with the assignment in Section 2.1.
• Thursday, March 4. Read Section 2.2 and work problems 4, 5, 7, 12, 15, 18, 20, 24-29, 33, 35.

Week 9

• Tuesday, March 9. Read Section 2.4 and work problems 7, 8-13, 19, 20, 25, 29.
• Thursday, March 11. Continue with the assignment in Section 2.4.

Week 10

• Tuesday, March 16. Spring Break, no class.
• Thursday, March 18. Spring Break, no class.

Week 11

• Tuesday, March 23.
• Thursday, March 25.

Week 12

• Tuesday, March 30.
• Thursday, April 1.

Week 13

• Tuesday, April 6. Honors Day, no class.
• Thursday, April 8. Test 2

Week 14

• Tuesday, April 13.
• Thursday, April 15.

Week 15

• Tuesday, April 20.
• Thursday, April 22.

Week 16

• Tuesday, April 27.
• Thursday, April 29.

Week 16

• Tuesday, May 4.
• Thursday, May 6. Final Exam