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Probability and Random Variables >> Content Detail



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Readings

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Readings are assigned in the required textbook: Amazon logo Ross, Sheldon. A First Course in Probability. 7th ed. Upper Saddle River, NJ: Prentice Hall, 2005. ISBN: 0131856626. Some supplemental readings are also provided.


Lec #TopicsReadings
1-3Combinatorial AnalysisRead Chapter 1
4-6Axioms of Probability, Conditional Probability and IndependenceRead Chapters 2 and 3

Sec. 3.1-3.2: Introduction, Conditional Probabilities
7-9Conditional Probability and Independence (cont.), Random VariablesRead 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
10-12Random 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)
13-15Continuous Random VariablesRead Chapter 5

Sec. 5.1-5.4: Introduction, Expectation and Variance of Continuous Random Variables, The Uniform Random Variable, Normal Random Variables
16-18Continuous 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.)
19-21Jointly Distributed Random VariablesRead 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)
22-24Properties of ExpectationRead Chapter 7

Sec. 7.1-7.4: Introduction, Expectation of Sums of Random Variables, Covariance, Variance of Sums, and Correlations, Conditional Expectation
25-28Limit TheoremsRead 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
29-32Additional Topics in Probability, SimulationRead Chapters 9 and 10

Sec. 9.1: The Poisson Process

Sec. 10.1-10.2: Introduction, General Techniques for Simulating Continuous Random Variables

 








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