Readings

Textbooks

Required

Buy at Amazon [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.

Buy at Amazon [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