This section includes assigned readings from the three main texts used in the course.

### Required Text

[ROS]: Ross, Sheldon M. *Probability and Statistics for Engineers and Scientists*. 3rd ed. San Diego, CA: Academic Press, 2004. ISBN: 0125980574.

### Recommended Texts

[LM]: Larsen, Richard J., and Morris L. Marx. *An Introduction to Mathematical Statistics and its Applications*. 3rd ed. Upper Saddle River, NJ: Prentice Hall, 2001. ISBN: 0139223037.

[DS]: DeGroot, Morris H., and Mark J. Schervish. *Probability and Statistics*. 3rd ed. Boston, MA: Addison-Wesley, 2002.

Larsen and Marx’s book is a bit more chatty than Ross’, while DeGroot and Schervish’s is a very good book but somewhat more difficult. You can find additional resources in the related resources section.

### Assigned Readings

Readings are from Ross [ROS], Larsen and Marx [LM], and DeGroot and Schervish [DS]. Note that ROS does not cover all the topics but more closely follows the material taught in class.

WEEK # | TOPICS | ROS | LM | DS |
---|---|---|---|---|

1 | Set and Probability Theory | Chapter 3 | Chapters 1.1–1.3, 2.1–2.10 | Chapters 1, 2.1–2.3 |

2 | Random Variables, Probability Mass/Density Function, Cumulative Distribution Function (Univariate Model) | Chapters 4.1–4.2, 5.1, pp. 160-1 | Chapter 3.1–3.4 | Chapter 3.1–3.3 |

3 | Multiple Random Variables, Bivariate Distribution, Marginal Distribution, Conditional Distribution, Independence, Multivariate Distribution (Multivariate Model) | Chapter 4.3 | Chapter 3.5–3.6, 3.9 | Chapter 3.4–3.7 |

4 | Expectation (Moments) | Chapter 4.4–4.9 | Chapter 3.10–3.13, 3.15–3.16 | Chapter 4.1–4.7 |

5 | Review for Exam 1 | |||

6 | Random Variable and Random Vector Transformations (Univariate and Multivariate Models) | Chapter 3.7 | Chapter 3.8–3.9 | |

7 | Special Distributions (Discrete and Continuous) | Chapter 5.1–5.8 | Chapters 3.3, 4.1–4.3, 4.5–4.6 | Chapter 5.1–5.6, 5.9 |

8 | Review for Exam 2 | |||

9 | Random Sample, Law of Large Numbers, Central Limit Theorem | Chapters 6, 4.9, 1, 2 | Chapters 3.14, pp. 272-5, 5.1, 5.4 | Chapters 4.8, 5.7, 7.1, 7.7 |

10 | Point Estimators and Point Estimation Methods | Chapter 7.7 and 7.1–7.2 | Chapter 5.2 | Chapter 6.5–6.6 |

11 | Interval Estimation and Confidence Intervals | Chapters 7.3–7.6, 5.8.2–5.8.3 | Chapter 5.3 | Chapter 7.5 |

12 | Hypothesis Testing | Chapter 8 | Chapters 6, 9.1–9.2 | Chapter 8 |

13 | Review for Exam 3 |

Advanced topics, time permitting: Bayesian Analysis and Nonparamatric Methods.