Textbooks
Required
[LM] = Larsen, R., and M. Marx. Introduction to Mathematical Statistics and Its Applications. 4th ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2005. ISBN: 9780131867932.
Recommended
[DS] = DeGroot, M., and M. Schervish. Probability and Statistics. 3rd ed. Reading, MA: Addison-Wesley, 2001. ISBN: 9780201524888.
[L] = Lindgren, B. Statistical Theory. 4th ed. New York, NY: Chapman and Hall, 1993. ISBN: 9780412041815.
| SES # | TOPICS | READINGS |
|---|---|---|
Probability distributions and random variables | ||
| I. Probability | ||
| 1 | Sets and events |
[LM] sections 1.1-1.3 and 2.1-2.7. [DS] sections 1.1-1.11 and 2.1-2.2. [L] sections 1.1-1.3. |
| 2 | Probabilities and counting rules | |
| 3 | Conditional probability and independence | |
| II. Random variables and distribution functions | ||
| 4 | Bayes theorem and random variables |
[LM] sections 3.1-3.4 and 3.7. [DS] sections 3.1-3.4 and 3.7. [L] section 2.1. |
| 5 | Discrete and continuous random variables | |
| 6 | Probability distribution functions (PDFs), cumulative distribution functions (CDFs), joint distribution of 2 or more random variables | |
| 7 | Joint and marginal distributions | |
| 8 | Review | |
Expectations and transformations of random variables | ||
| III. Transformations of random variables | ||
| 9 | Functions of random variables |
[LM] sections 3.8-3.10. [DS] sections 3.8-3.9. [L] section 2.1.6. |
| 10 | Functions of several random variables | |
| IV. Expectations and conditional distributions | ||
| 11 | Order statistics and expectations |
[LM] sections 3.5-3.6 and 3.11. [DS] sections 3.6 and 4.1-4.7. [L] sections 2.1.8 and 2.2. |
| 12 | Median, quantiles, and variance | |
| 13 | Covariance and conditional expectations | |
| V. Special distributions | ||
| 14 | Conditional expectations and special distributions |
[LM] chapter 4. [DS] chapter 5, except 5.7-5.8. [L] chapter 3. |
| VI. Law of large numbers and central limit theorems | ||
| 15 | Law of large numbers |
[LM] section 4.3. [DS] section 5.7. [L] section 2.5. |
| 16 | Review | |
Estimation and hypothesis tests | ||
| VII. Estimation methods and properties | ||
| 17 | Central limit theorem, estimators, bias, and consistency |
[LM] sections 5.1-5.5 and 5.7. [DS] sections 6.1 and 6.5-6.7. [L] sections 5.1-5.2. |
| 18 | Constructing estimators | |
| VIII. Confidence intervals | ||
| 19 | Confidence intervals |
[LM] section 5.3. [DS] section 7.5. [L] section 5.3. |
| 20 | Confidence intervals (cont.) | |
| IX. Hypothesis testing | ||
| 21 | Hypothesis tests |
[LM] sections 6.1-6.5, 7.1-7.5, and 9.1-9.4. [DS] chapter 8. [L] sections 6.1-6.2. |
| 22 | Hypothesis tests (cont.) | |
| 23 | Hypothesis tests (cont.) | |
| 24 | Review | |