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.
Course readings and files.
| 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 |