MA 385-01, Fall 2009

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

• Monday, 8:00 - 9:00
• Tuesday, 12:45 - 2:15
• Wednesday, 8:00 - 9:00
• Thursday, 12:45 - 2:15
• Friday, 8:00 - 9:00

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: Introduction to Probability (http://www.math.uah.edu/siegrist/MA385/GrinsteadSnell.pdf), by Charles M. Grinstead and J. Laurie Snell, with solutions to odd numbered exercises (http://www.math.uah.edu/siegrist/MA385/GrinsteadSnellSolutions.pdf).
• 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. If you would like a copy of the entire Virtual Labs site for use offline, plese bring me either a blank, writeable CD or a thumb drive with 100 MB of free space.

Course Outline

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

Class Schedule

• Tuesday, Thursday 2:20 - 3:40
• 205 Shelby Center

Grade Determination

• Quizzes and graded homework: 2/3
• Final Exam: 1/3

For the graded homework, be sure to show all relevant work and justify your answers. Use correct notation and methods. Remember that it's the process that is important, not the answer.

Final Exam:

• Tuesday, December 8, 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.

Quizzes

Quizzes

• Quiz 0
• Quiz 1
• Quiz 2
• Quiz 3
• Quiz 4
• Quiz 5

Assignments

Week 1

• Thursday, August 20. Set up the course materials. Read Section 1 on Random Experiments in Chapter 2 on Probability Spaces.

Week 2

• Tuesday, August 25. Read Section 2 on Events and Random Variables in Chapter 2 on Probability Spaces. Work problems 21, 23, 25, 26, 27, 29, 32.
• Thursday, August 27. Read Section 1.7 (Counting Measure) and work problems 16, 17, 19, 20, 21, 23, 24, 25.

Week 3

• Tuesday, September 1. Read Section 1.8 and work problems 25-40.
• Thursday, September 3. Read Section 2.3 (Probability Measure) through Exercise 20. Work problems 29-34, 36, 37, 39, 40.

Week 4

• Tuesday, September 8. Continue with Section 2.3. Work problems 41, 42, 44, 51-53, 55, 57, 58.
• Thursday, September 10. Read Section 2.4 through exercise 6. Work problems 7-15, 17, 20, 22, 23.

Week 5

• Tuesday, September 15. Continue with Section 2.4. Work problems 28-34, 36, 39-42.
• Thursday, September 17. Read Section 2.5. Work problems 20, 21, 22, 24, 25, 26, 28, 29, 31, 32, 33, 34.

Week 6

• Tuesday, September 22. Continue with Section 2.5. Work problems 38-43, 45, 46-50, 51, 52.
• Thursday, September 24. Hand in problems 28, 36, 40 in Section 2.4 and problems 21, 48, 52 in Section 2.5 next Tuesday. Read Section 3.1 and begin working problems 8, 13, 15-22, 24, 26-28, 33, 35, 36, 39, 40, 45-47.

Week 7

• Tuesday, September 29. Continue with the assignment in Section 3.1.
• Thursday, October 1. Hand in problem 51 in Section 2.5 and problems 22, 35, 46, and 48 in Section 3.1 next Tuesday. In Section 3.2, read the Basic Theory and begin working problems 4-8, 12-29.

Week 8

• Tuesday, October 6. Continue the assignment in Section 3.2. Hand in problems 7, 12, 18, 25, 29 in Section 3.2 on Tuesday.
• Thursday, October 8. Fall Break; no class

Week 9

• Tuesday, October 13. Read Section 3.4 and work problems 1-13, 19, 20, 25, 29
• Thursday, October 15. Read Section 3.5 and work problems 9-15, 17, 19-24, 26, 28, 31, 34. Hand in problems 7, 9, 10, 12, 20 in Section 3.4 next Tuesday.

Week 10

• Tuesday, October 20. Continue with the assignment in Section 3.5.
• Thursday, October 22. Hand in problems 9, 21, 22, 24, 31 in Section 3.5 next Thursday. In Section 3.6 work problems 26, 27, 29, 30, 32, 34, 38, 41, 42.

Week 11

• Tuesday, October 27. Continue with the assignment in Section 3.6. In Section 3.7, work the basic theory.
• Thursday, October 29. Work problems 25, 29, 41, 43, 44, 50, 51, 52, 53, 55, 58 in Section 3.7. On Thursday 11/5, hand in problems 32 (a, d, e, f) and 41 in Section 3.6 and problems 50, 51, 58 in Section 3.7.

Week 12

• Tuesday, November 3. Read the basic theory. Start problems 12-33.
• Thursday, November 5. Continue with Section 4.1. Work problems 12-33, 36-50. Next Thursday, hand in problem 43 in Section 3.7 and problems 36, 38, 48, 49 in Section 4.1.

Week 13

• Tuesday, November 10. Read the basic theory in Section 4.2 and work problems 10-14, 17, 19, 22, 25, 27, 28, 30, 31, 33.
• Thursday, November 12. Read the basic theory in Section 4.3 and work problems 27, 29, 30, 31, 36, 40, 41, 43-46, 47, 48, 50, 51. Next Thursday, hand in problems 15, 30 (a, b, c), 31 in Section 4.2.

Week 14

• Tuesday, November 17. Continue with the assignment in Section 4.3.
• Thursday, November 19. Hand in problems 29, 43, 44, 45 in Section 4.3 next Tuesday.

Week 15

• Tuesday, November 24.
• Thursday, November 26. Thanksgiving; no class

Week 16

• Tuesday, December 1.