Introduction to Probability Theory
Schedule
Week
| Date | Topic | ||
| 1 | Th 09/22 | Review of the course syllabus. Introduction and basic concepts. Sections 1.1-1.4. | Set Theory Solutions |
| 2 | Tu 09/27 | Definition of probability and finite sample spaces. Sections 1.5-1.6. | |
| Th 09/29 | Counting methods. Combinatorial methods. Sections 1.7-1.8. | Counting Solutions |
|
| 3 | Tu 10/04 | Union of events. Conditional probability and independent events. Sections 1.10 and 2.1-2.2. | Cond Prob Solutions |
| Th 10/06 | Bayes' Theorem. Section 2.3. | ||
| 4 | Tu 10/11 | Discrete random variables. Examples of discrete random variables. Sections 3.1, 5.1-5.5. Quiz #1. |
|
| Th 10/13 | Examples of discrete random variables. Sections 5.1-5.5 | Dscrt RV Solutions |
|
| 5 | Tu 10/18 | Continuous random variables. The CDF. Sections 3.2-3.3. | Cnt RV Solutions |
| Th 10/20 | Bivariate distributions and marginal distributions. Sections 3.4 and 3.5. | Biv RV Solutions |
|
| 6 | Tu 10/25 | Review | |
| Th 10/27 | Midterm | ||
| 7 | Tu 11/1 | Conditional distributions. Section 3.6 | |
| 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 | Covariance and conditional expectation. Sections 4.6-4.7. Quiz #2. |
|
| 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. Quiz #3 (optional). |
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| Mo 12/05 | Final (two hours: 9:00 to 11:00) |
| Attachment | Size |
|---|---|
 fnct.pdf | 88.76 KB |
| exp.pdf | 93.56 KB |
| cnddr.pdf | 87.24 KB |
| normal.pdf | 71.23 KB |
| soluc_fnct.pdf | 98.5 KB |
| soluc_cnddr.pdf | 95.38 KB |
| soluc_exp.pdf | 98.21 KB |