## 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 |
---|---|---|

| ||

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 | |

| ||

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 | |

| ||

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 |