We will cover basic probability theory, starting with combinatorial analysis, then covering probability rules, continuous & discrete random variables, expectation. If time permits, we may investigate Markov chains, Chebyshev's inequality, and the Law of Large numbers.
The schedule below is tentative, and may be subject to change. Changes will be announced in class, and you are responsible for knowing about any changes even if you miss the class when they are announced.
| Week | Dates | Topic | Homework |
|---|---|---|---|
| 1 | Aug 21 - Aug 25 | Permutations & Combinations | Chapter 1 |
| 2 | Aug 28 - Sep 1 | The Binomial Theorem | |
| 3 | Sep 4 - Sep 8 | Axioms of Probability | Chapter 2 |
| 4 | Sep 11 - Sep 15 | Equiprobable Spaces | Generating Functions |
| 5 | Sep 18 - Sep 22 | Conditional Probability | Chapter 3 |
| 6 | Sep 25 - Sep 29 | Independence | |
| 7 | Oct 2 - Oct 6 | Discrete Random Variables | Chapter 4 |
| 8 | Oct 11 - Oct 13 | Expectation & Variance | |
| 9 | Oct 16 - Oct 20 | Bernoulli & Poisson Distributions | |
| 10 | Oct 23 - Oct 27 | Continuous Random Variables | Chapter 5 |
| 11 | Oct 30 - Nov 3 | Normal & Exponential Distributions | |
| 12 | Nov 6 - Nov 10 | Joint Distributions | Chapter 6 |
| 13 | Nov 13 - Nov 17 | Joint Distributions - con'd | |
| 14 | Nov 20 | Properties of Expectation | |
| 15 | Nov 27 - Dec 1 | Moment Generating Functions |
Attendance in this class is required. Repeated absences may result in a forced withdrawal from the course. You are responsible for any material you miss due to absence. Please let me know ahead of time if you know that you will not be able to attend class.
The term grade will be based on the following factors.
| Component | Proportion |
|---|---|
| Homework | 40% |
| Quizzes | 30% |
| Final Exam | 30% |
I will assign homework problems every day in class. You should keep your solutions to these problems in a homework notebook. From time to time, I will ask to see your solutions to assigned problems. Usually, you will present solutions in class, although sometimes you may need to present solutions outside of class time, during office hours for example. Each homework problem will be graded on a simple two point scale:
I encourage you to work with the other students on the homework, but you must have a clear understanding of your solutions to get credit.
Your letter grade for homework will be determined by the total number of problems from the book you are able to solve.
About once a month, there will be a quiz to test your understanding of the material. These quizzes will be announced in advance, and you will know exactly what concepts will be covered on each quiz. You will not be asked to write proofs during the quizzes, instead the quizzes will focus on definitions, concepts and knowledge about probability. Each quiz will take about 20 minutes.
There will be a cumulative final exam. It will include questions similar to the ones on the quizzes, as well as a few more challenging problems similar to the ones on the homework.
In compliance with the Hampden-Sydney College policy and equal access laws, I am available to discuss appropriate academic accommodations that may be recommended for students with disabilities. Requests for academic accommodations are to be made at the beginning of the semester (except for unusual circumstances) so that appropriate arrangements can be made. Students are required to contact the Office of Academic Success in order to verify their eligibility for appropriate accommodations. How does this look?