### Probability

Fall 2011

Thursdays 4-6:50 p.m.

Millikan 134 (Pomona College)

**Instructor:** Professor Allon Percus

**Contact information:** CGU Math South Building, tel. 909-607-0744

**Office hours:** Mondays 10:15-11:45am (or by appointment) at CGU Math South

**TAs:**

- Bo Yan, bo.yan@cgu.edu
- Yuan Li, liyuanayu@gmail.com

The TAs will run a weekly problem session Wednesdays 2-4pm in McManus 31. This is one of the rooms directly below Hagelbarger’s.

**Course description:** Math 251 covers the main elements of probability theory at an intermediate level. Topics include combinatorial analysis, conditional probabilities, discrete and continuous random variables, probability distributions, central limit theorem, and numerous applications.

**Textbook:** Sheldon Ross, *A First Course in Probability*, 8th ed. (Prentice Hall, Upper Saddle River, NJ, 2010).

**Assignments and grading:** Homework assignments will be due each week on Thursdays. They may be turned in physically during class, or electronically to the TA by midnight (by e-mail to bo.yan@cgu.edu or submitted through sakai). Late homework will not be accepted without prior approval. There will be a midterm and a final exam. Grades will be calculated as follows:

- 30% Homework
- 30% Midterm exam
- 40% Final exam

You may work together on homework assignments, but all your answers must be explained in your own words. *Your homework submission must also state the names of all those with whom you collaborated.* Please familiarize yourselves with CGU’s academic honesty policies.

**Tentative schedule:**

- Sep 1: Combinatorial analysis (Chapter 1)
- Sep 8: Multinomial coefficients; sample spaces and events (Chapters 1 & 2)
- Sep 15: Equally likely outcomes; conditional probabilities (Chapters 2 & 3)
- Sep 22: Bayes’ rule; independent events; discrete random variables (Chapters 3 & 4)
- Sep 29: Expectation; variance; probability distributions (Chapter 4)
- Oct 6: Continuous random variables (Chapter 5)
- Oct 13: Probability density functions (Chapter 5)
- Oct 20: REVIEW AND MIDTERM EXAM
- Oct 27: Joint distributions (Chapter 6)
- Nov 3: Conditional distributions (Chapter 6)
- Nov 10: Moments of distributions (Chapter 7)
- Nov 17: More on moments; law of large numbers (Chapters 7 & 8)
- Nov 24: HOLIDAY (THANKSGIVING)
- Dec 1: Central limit theorem; additional topics (Chapters 8 & 9)
- Dec 8: REVIEW
- Dec 15: FINAL EXAM