| Week | Lecture dates | Sections | topics |
|---|---|---|---|
| 1 | 1/24 (Thurs) | 1.1-1.6 | Combinatorics |
| 2 | 1/28, 1/31 | 2.1-2.5 | Axioms of probability; Inclusion/exclusion formula; Equally likely outcomes |
| 3 | 2/4, 2/7 | 2.5, 3.1-3.3 |
More examples; Stirling's approximation; Conditional probability and Bayes' formula |
| 4 | 2/11, 2/14 | 3.4-3.5 | Independent events, Repeated independent trials |
| 5 | 2/18, 2/21 | 4.1-4.5, 4.9 | Discrete random variables and distribution functions; Expectation and variance |
| 6 | 2/25, 2/28 | 4.6-4.10 | Special Random variables: Bernoulli, binomial, Poisson, geometric, negative binomial, and hypergeometric random variables |
| 7 | 3/4, 3/7 | Review, EXAM 1 | Covers work on this syllabus through Chapter 4 |
| 8 | 3/11, 3/14 | 5.1--5.5 |
Continuous random variables and distribution functions; Uniform, exponential and normal distributions |
| 8+ | 3/16-3/24 | SPRING BREAK | individual |
| 9 | 3/25, 3/29 | 5.6.1, 5.7, 6.1 |
Gamma random variable; functions of a random variable; Joint distributions of several random variables |
| 10 | 4/1, 4/4 | 6.2-6.3 | Independent random variables and their sums |
| 11 | 4/8, 4/11 | 7.1, 7.2, 7.4 | Linearity of expectation; covariance and correlation |
| 12 | 4/15, 4/18 | EXAM 2 | Covers work on this syllabus covered since Exam 1 |
| 13 | 4/22, 4/25 | 6.4, 6.5, 7.5, 7.7 | Conditional expectation; conditional distributions; moment generating functions |
| 14 | 4/29, 5/2 | 8.1-8.3 |
Markov and Chebyshev inequalities; weak law of large numbers; Central Limit Theorem |
| 15 | 5/6 (Mon.) | 8.3 | Proof of the central limit theorem; examples; review. |
| FINAL | 5/9 | 8:00--11:00 AM | The exam will be cumulative, and will be in SEC-211 |
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.