Research Catalog

Title

A first course in probability / Sheldon Ross.

Author

Ross, Sheldon M.

Publication

Upper Saddle River, N.J. : Pearson Prentice Hall, [2006], ©2006.

Items in the Library & Off-site

Holdings

Details

Description

x, 565 pages : illustrations; 25 cm

Subject

• Probabilities > Textbooks

Note

• Includes index.

Contents

1. Combinatorial Analysis -- 1.1. Introduction -- 1.2. The Basic Principle of Counting -- 1.3. Permutations -- 1.4. Combinations -- 1.5. Multinomial Coefficients -- 1.6. The Number of Integer Solutions of Equations* -- 2. Axioms of Probability -- 2.1. Introduction -- 2.2. Sample Space and Events -- 2.3. Axioms of Probability -- 2.4. Some Simple Propositions -- 2.5. Sample Spaces Having Equally Likely Outcomes -- 2.6. Probability as a Continuous Set Function* -- 2.7. Probability as a Measure of Belief -- 3. Conditional Probability and Independence -- 3.1. Introduction -- 3.2. Conditional Probabilities -- 3.3. Bayes' Formula -- 3.4. Independent Events -- 3.5. P(.[vertical bar]F) Is a Probability -- 4. Random Variables -- 4.1. Random Variables -- 4.2. Discrete Random Variables -- 4.3. Expected Value -- 4.4. Expectation of a Function of a Random Variable -- 4.5. Variance -- 4.6. The Bernoulli and Binomial Random Variables -- 4.6.1. Properties of Binomial Random Variables -- 4.6.2. Computing the Binomial Distribution Function -- 4.7. The Poisson Random Variable -- 4.7.1. Computing the Poisson Distribution Function -- 4.8. Other Discrete Probability Distributions -- 4.8.1. The Geometric Random Variable -- 4.8.2. The Negative Binomial Random Variable -- 4.8.3. The Hypergeometric Random Variable -- 4.8.4. The Zeta (or Zipf) Distribution -- 4.9. Properties of the Cumulative Distribution Function -- 5. Continuous Random Variables -- 5.1. Introduction -- 5.2. Expectation and Variance of Continuous Random Variables -- 5.3. The Uniform Random Variable -- 5.4. Normal Random Variables -- 5.4.1. The Normal Approximation to the Binomial Distribution -- 5.5. Exponential Random Variables -- 5.5.1. Hazard Rate Functions -- 5.6. Other Continuous Distributions -- 5.6.1. The Gamma Distribution -- 5.6.2. The Weibull Distribution -- 5.6.3. The Cauchy Distribution -- 5.6.4. The Beta Distribution -- 5.7. The Distribution of a Function of a Random Variable -- 6. Jointly Distributed Random Variables -- 6.1. Joint Distribution Functions -- 6.2. Independent Random Variables -- 6.3. Sums of Independent Random Variables -- 6.4. Conditional Distributions: Discrete Case -- 6.5. Conditional Distributions: Continuous Case -- 6.6. Order Statistics -- 6.7. Joint Probability Distribution of Functions of Random Variables -- 6.8. Exchangeable Random Variables -- 7. Properties of Expectation -- 7.1. Introduction -- 7.2. Expectation of Sums of Random Variables -- 7.2.1. Obtaining Bounds from Expectations via the Probabilistic Method -- 7.2.2. The Maximum-Minimums Identity -- 7.3. Moments of the Number of Events that Occur -- 7.4. Covariance, Variance of Sums, and Correlations -- 7.5. Conditional Expectation -- 7.5.1. Definitions -- 7.5.2. Computing Expectations by Conditioning -- 7.5.3. Computing Probabilities by Conditioning -- 7.5.4. Conditional Variance -- 7.6. Conditional Expectation and Prediction -- 7.7. Moment Generating Functions -- 7.7.1. Joint Moment Generating Functions -- 7.8. Additional Properties of Normal Random Variables -- 7.8.1. The Multivariate Normal Distribution -- 7.8.2. The Joint Distribution of the Sample Mean and Sample Variance -- 7.9. General Definition of Expectation -- 8. Limit Theorems -- 8.1. Introduction -- 8.2. Chebyshev's Inequality and the Weak Law of Large Numbers -- 8.3. The Central Limit Theorem -- 8.4. The Strong Law of Large Numbers -- 8.5. Other Inequalities -- 8.6. Bounding The Error Probability -- 9. Additional Topics in Probability -- 9.1. The Poisson Process -- 9.2. Markov Chains -- 9.3. Surprise, Uncertainty, and Entropy -- 9.4. Coding Theory and Entropy -- 10. Simulation -- 10.1. Introduction -- 10.2. General Techniques for Simulating Continuous Random Variables -- 10.2.1. The Inverse Transformation Method -- 10.2.2. The Rejection Method -- 10.3. Simulating from Discrete Distributions -- 10.4. Variance Reduction Techniques -- 10.4.1. Use of Antithetic Variables -- 10.4.2. Variance Reduction by Conditioning -- 10.4.3. Control Variates -- A. Answers to Selected Problems -- B. Solutions to Self-Test Problems and Exercises.

ISBN

0131856626

LCCN

2005047691

OCLC

• ocm59401216
• SCSB-5198719

Owning Institutions

Columbia University Libraries