Week |
Date |
Topic |
1 |
Th 09/22 |
Review of the course syllabus. Introduction and basic concepts. Sections 1.1-1.4. Kadane: 1.1 |
2 |
Tu 09/27 |
Definition of probability and finite sample spaces. Sections 1.5-1.6. Kadane: 1.2,1.3. |
|
Th 09/29 |
Counting methods. Combinatorial methods. Multinomial coefficients. Sections 1.7-1.9. |
3 |
Tu 10/04 |
Union of events. Conditional probability and independent events. Sections 1.10 and 2.1-2.2. Kadane: 2.1, 2.2, 2.3 |
|
Th 10/06 |
Bayes' Theorem. Section 2.3. Kadane: 2.4, 2.5, 2.6 |
4 |
Tu 10/11 |
Discrete random variables. Examples of discrete random variables. Sections 3.1, 5.1-5.5. |
|
Th 10/13 |
Examples of discrete random variables. Continuous random variables. The CDF. Sections 5.1-5.5, and 3.2-3.3. |
5 |
Tu 10/18 |
Bivariate distributions and marginal distributions. Sections 3.4 and 3.5. |
|
Th 10/20 |
Conditional distributions. Section 3.6 |
6 |
Tu 10/25 |
Review |
|
Th 10/27 |
MIDTERM |
7 |
Tu 11/1 |
Multivariate distributions. Section 3.7. |
|
Th 11/3 |
Functions of random variables. Sections 3.8-3.9. |
8 |
Tu 11/8 |
Markov chains. Section 3.10 |
|
Th 11/10 |
Expectation and variances. Section 4.1-4.3 and 5.1-5.5. |
9 |
Tu 11/15 |
Moment generating functions. Covariance and conditional expectation. Sections 4.4-4.6. |
|
Th 11/17 |
The normal distribution. Markov and Chebyshev's inequalities. The law of large numbers. Sections 5.6, 6.1-6.2. |
10 |
Tu 11/22 |
The law of large numbers and the central limit theorem. Sections 6.2-6.3 |
|
Th 11/24 |
THANKSGIVING |
11 |
Tu 11/29 |
More CLT examples. Other distributions: the gamma and beta distributions. The Poisson process. |
|
Th 12/01 |
Review. |
|
Mo 12/05 |
FINAL EXAM (two hours: 1 - 3 PM) |