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Texts
Required
Larsen, Richard, and Morris Marx. Introduction to Mathematical Statistics and its Applications. 3rd ed. Upper Saddle River, NJ: Prentice Hall, 2000. ISBN: 0139223037.
It's easier than the level of the course, but I think it provides pretty good discussions.
Recommended
DeGroot, Morris, and Mark Schervish. Probability and Statistics. Reading, MA: Addison-Wesley, 2001. ISBN: 0201524880.
DeGroot is a good but somewhat more difficult book.
Lindgren, Bernard. Statistical Theory. New York, NY: Chapman and Hall, 1993. ISBN: 0412041812.
Lindgren doesn't offer much intuition, but it's a nice reference.
Readings by Week
Readings are from Larsen and Marx (L&M), DeGroot (D), and Lindgren (L).
Readings.
| WEEK # |
TOPICS |
READINGS |
| 1-2 |
Probability |
L&M, 1.1-1.3, and 2.1-2.9
D, 1.1-1.11, and 2.1-2.2
L, 1.1-1.3 |
| 3-4 |
Random Variables, Distribution Functions |
L&M, 3.1-3.4
D, 3.1-3.4, and 3.7
L, 2.1 |
| 5-6 |
Random Variable Transformations |
L&M, 3.5-3.6
D, 3.8-3.9
L, 2.1.6 |
| 7-8 |
Conditional Distributions, Expectations |
L&M, 3.7-3.13
D, 3.6, and 4.1-4.7
L, 2.1.8, and 2.2 |
| 9-10 |
Special Distributions |
L&M, chapter 4
D, chapter 5, and ex. 5.7-5.8
L, chapter 3 |
| 11-12 |
Law of Large Numbers, Limit Theorems |
L&M, 7.3-7.4
D, 5.7
L, 2.5 |
| 13-14 |
Estimation Methods, Properties |
L&M, 5.1-5.8, and 7.2
D, 6.1, and 6.5-6.7
L, 5.1-5.2 |
| 15 |
Confidence Intervals |
L&M, 5.9-5.10
D, 7.5
L, 5.3 |
| 16 |
Hypothesis Testing
Advanced Topics, Time Permitting Bayesian Analysis, Nonparametric Methods |
L&M, 6.1-6.4, 7.5-7.7, and 8.1-8.5
D, chapter 8
L, 6.1-6.2 |
| 17 |
Exam Week |
|