| Week | Lecture dates | Sections | topics |
|---|---|---|---|
| 1 | 1/20 (Thurs) | 1.1-1.6 | Combinatorics |
| 2 | 1/24, 1/27 | 2.1-2.5 | Axioms of probability; inclusion/exclusion formula;Equally likely outcomes |
| 3 | 1/31, 2/3 | 2.5, 3.1-3.3 |
More examples; Stirling's approximation; Conditional probability and Bayes' formula |
| 4 | 2/7, 2/10 | 3.4-3.5 | Independent events, Repeated independent trials |
| 5 | 2/14, 2/17 | 4.1-4.5, 4.9 | Discrete random variables and distribution functions; Expectation and variance |
| 6 | 2/21, 2/24 | 4.6-4.10 | Special Random variables: Bernoulli, binomial, Poisson, geometric, negative binomial, and hypergeometric random variables |
| 7 | 2/28, 3/3 | Review, EXAM 1 | Covers work on this syllabus through Chapter 4 |
| 8 | 3/7, 3/10 | 5.1--5.5 |
Continuous random variables and distribution functions; Uniform, exponential and normal distributions |
| 8+ | 3/12-3/20 | SPRING BREAK | individual |
| 9 | 3/21, 3/24 | 5.6.1, 5.7, 6.1 |
Gamma random variable; functions of a random variable; Joint distributions of several random variables |
| 10 | 3/28, 3/31 | 6.2-6.3 | Independent random variables and their sums |
| 11 | 4/4, 4/7 | 7.1, 7.2, 7.4 | Linearity of expectation; covariance and correlation |
| 12 | 4/11, 4/14 | EXAM 2 | Covers work on this syllabus covered since Exam 1 |
| 13 | 4/18, 4/21 | 6.4, 6.5, 7.5, 7.7 | Conditional expectation; conditional distributions; moment generating functions |
| 14 | 4/25, 4/28 | 8.1-8.3 |
Markov and Chebyshev inequalities; weak law of large numbers; Central Limit Theorem |
| 15 | 5/2 (Mon.) | 8.3 | Proof of the central limit theorem; examples. |
| FINAL | 5/11 (Wed) | 12:00--3 PM | The exam will be cumulative, and will be in ARC 205 |
Syllabus in Catalogue: Basic probability theory in both discrete and continuous sample spaces, combinations, random variables and their distribution functions, expectations, law of large numbers, central limit theorem.
Charles Weibel / Spring 2011