| Lec # | Topics | Readings |
|---|---|---|
| 1-3 | Combinatorial Analysis | Read Chapter 1 |
| 4-6 | Axioms of Probability, Conditional Probability and Independence | Read Chapters 2 and 3 Sec. 3.1-3.2: Introduction, Conditional Probabilities |
| 7-9 | Conditional Probability and Independence (cont.), Random Variables | Read Chapters 3 and 4 Sec. 3.3-3.5: Bayes' Formula, Independent Events, P(•|F) is a Probability Sec. 4.1-4.3: Random Variables, Discrete Random Variables, Expected Value |
| 10-12 | Random Variables (cont.) | Read Chapter 4 Sec. 4.4-4.7: Expectation of a Function of a Random Variable, Variance, The Bernoulli and Binomial Random Variables, The Poisson Random Variable Sec. 4.8.1, 4.8.3: The Geometric Random Variable, The Hypergeometric Random Variable Stirling's Formula Notes (PDF) |
| 13-15 | Continuous Random Variables | Read Chapter 5 Sec. 5.1-5.4: Introduction, Expectation and Variance of Continuous Random Variables, The Uniform Random Variable, Normal Random Variables |
| 16-18 | Continuous Random Variables (cont.) | Read Chapter 5 Sec. 5.5-5.7: Exponential Random Variables, Other Continuous Distributions, The Distribution of a Function of a Random Variable Beta Distribution Notes (PDF) (Courtesy of Robert J. Holt, Richard M. Dudley, and Lewis Pakula. Used with permission.) |
| 19-21 | Jointly Distributed Random Variables | Read Chapter 6 Sec. 6.1-6.5: Joint Distribution Functions, Independent Random Variables, Sums of Independent Random Variables, Conditional Distributions: Discrete Case, Conditional Distributions: Continuous Case Sec. 6.7: Joint Probability Distribution of Functions of Random Variables Problem Set 7 Material (PDF) |
| 22-24 | Properties of Expectation | Read Chapter 7 Sec. 7.1-7.4: Introduction, Expectation of Sums of Random Variables, Covariance, Variance of Sums, and Correlations, Conditional Expectation |
| 25-28 | Limit Theorems | Read Chapter 8 Sec. 8.1-8.5: Introduction, Chebyshev's Inequality and the Weak Law of Large Numbers, The Central Limit Theorem, The Strong Law of Large Numbers, Other Inequalities |
| 29-32 | Additional Topics in Probability, Simulation | Read Chapters 9 and 10 Sec. 9.1: The Poisson Process Sec. 10.1-10.2: Introduction, General Techniques for Simulating Continuous Random Variables |
Table of Contents
Study Materials
Readings
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Readings are assigned in the required textbook: Ross, Sheldon. A First Course in Probability. 7th ed. Upper Saddle River, NJ: Prentice Hall, 2005. ISBN: 0131856626. Some supplemental readings are also provided.