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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. ISBN: 0201524880.
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.
Course readings.
| 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.