Math 362, Theory of Probability - Fall 2015
Topics, Exams and Homework Assignments
| Week | Dates | Topics | Sections Covered | Homework | Due |
|---|---|---|---|---|---|
| 1 | Aug 24—Aug 28 | Probability in the World Around Us. Randomness with known and unknown structure. Introduction to R. | 1.1, 1.2, 1.3, 1.4, 1.5, 2.1, 2.2 | 2.2: 2.5, 2.7, 2.9, 2.13 R: R1 | Sep 2 |
| 2 | Aug 31—Sep 4 | Sample Spaces and Events. | 2.3 | 2.3: 2.17, 2.19, 2.21, 2.23 | Sep 9 |
| 3 | Sep 7 | Labor Day - no class. | R (Posted): R2 | Sep 30 | |
| 3 | Sep 9—Sep 11 | More on sets, sample spaces, events. Inclusion-Exclusion Principle for 2 sets and 3 sets (Example 2.2). | 2.2, 2.3 | Inclusion-Exclusion for 2/3 sets: Solve Example 2.2 and practice on similar problems. | Sep 16 |
| 4 | Sep 14—Sep 18 | Definition of Probability. Counting Rules Used in Probability. | 2.4, 2.5 | 2.4: 2.35, 2.37, 2.45, 2.48, 2.51, 2.53, 2.61, 2.5: 2.67, 2.69, 2.71 | Sep 21 |
| 5 | Sep 21 | Counting rules. Multi-stage processes. Two-way tables. Probability trees. Review for Midterm 1. | 2.4, 2.5 | R (Reminder): R2 | Sep 30 |
| 5 | Sep 23 | TAKE-HOME MIDTERM 1 POSTED. Counting Rules. Permutations, Combinations. Distinct vs. identical items. | 2.4, 2.5 | ||
| 5 | Sep 25 | Counting Rules used in Probability. Review of Take-Home Midterm 1 topics. Assignment R2. | |||
| 6 | Oct 6 | NOTE: This syllabus item is added purely to describe R Assignment 3. The topics in this assignment cover: counting rules, conditional probability, Bayes Formula, computing contingency tables with R, computing multinomial coefficients. First encounter of the multi-nomial distribution. | 2.4, 3.1, 3.2, 3.3 | R (Posted): R3 | Oct 21 |
| 6 | Sep 28—Oct 3 | Conditional Probability. Independence. Theorem on Total Probability and Bayes Rule. | 3.1, 3.2, 3.3 | 3.1: 3.5, 3.13, 3.15, 3.2: 3.27, 3.35, 3.37 | Oct 7 |
| 7 | Oct 5—Oct 9 | Theorem on Total Probability and Bayes Rule. | 3.3 | 3.3: 3.43, 3.45, 3.48, 3.49 | Oct 14 |
| 8 | Oct 12—Oct 16 | Random Variables and Their Probability Distributions. | 4.1 | 4.1: 4.1, 4.7, 4.8, 4.9, 4.12 | Oct 21 |
| 9 | Oct 19 | Review for Midterm 2. | |||
| 9 | Oct 21 | Midterm 2. | |||
| 9 | Oct 23 | Random Variables and Their Probability Distributions. The Bernoulli Distribution. The Binomial Distribution. | 4.1, 4.2, 4.3 | 4.2: 4.19, 4.23, 4.41 R (Posted): R4 | Oct 28 |
| 10 | Oct 26—Oct 30 | Independence of Random Variables. Distribution of a sum of independent random variables. Convolution of probability functions. Expected Value of Discrete Random Variables. Variance. | 4.4, 4.5, 4.6 | 4.4: 4.43, 4.49, 4.51, 4.61, 4.63, 4.6: 4.67, 4.72, 4.73, 4.78, 4.79 | Nov 4 |
| 11 | Nov 2—Nov 6 | Tchebysheff's Inequality. The Geometric Distribution. The Negative Binomial Distribution. The Poisson Distribution. The Hypergeometric Distribution. | 4.7, 4.8, 4.9, 4.10 | 4.7: 4.89, 4.101, 4.8: 4.109, 4.110, 4.9: 4.125, 4.126, 4.127, 4.128, 4.132, 4.135, 4.10: 4.139, 4.143 R (Due): R4 | Nov 11 |
| 12 | Nov 9—Nov 13 | The Moment-Generating Function. The Probabilty-Generating Function. | |||
| 12 | Nov 11 | Veteran's Day - no class. | |||
| 12 | The Moment-Generating Function. The Probabilty-Generating Function. | 4.11, 4.12 | |||
| 13 | Nov 23—Nov 27 | Continuous random Variables and Their Probability Distributions. | 5.1, 5.2 | ||
| 14 | Nov 30 | Review for Midterm 3. Expected Values of Continuous Random Variables. The Uniform Distribution. The Exponential Distribution. | 5.3, 5.4 | ||
| 14 | Dec 2 | Midterm 3. | |||
| 14 | Dec 4 | The Gamma Distribution. The Normal Distribution. | 5.5, 5.6 | 5.4: 5.41, 5.42, 5.43, 5.5: 5.65, 5.67, 5.6: 5.83, 5.85 R (Due): R5 | Dec 9 |
| 15 | Dec 7—Dec 9 | Expectation of Discontinuous functions and Mixed Probability Distributions. Review before the Final Exam. | |||
| Finals Week | Dec 15 (Tuesday) | Final Exam, 10:30 am - 12:30 pm (regular room). |