Research Catalog

Title

A first course in probability / Sheldon Ross.

Author

Ross, Sheldon M.

Publication

Upper Saddle River, N.J. : Prentice Hall, c2002.

Items in the Library & Off-site

Holdings

Details

Description

viii, 520 p. : ill.; 24 cm.

Subject

• Probabilities
• Probability
• Probability Theory

Note

• Includes index.

Processing Action (note)

• committed to retain

Contents

1 Combinatorial Analysis 1 -- 1.2 The Basic Principle of Counting 2 -- 1.3 Permutations 3 -- 1.4 Combinations 5 -- 1.5 Multinomial Coefficients 10 -- 1.6 The Number of Integer Solutions of Equations 12 -- 2 Axioms of Probability 24 -- 2.2 Sample Space and Events 24 -- 2.3 Axioms of Probability 28 -- 2.4 Some Simple Propositions 31 -- 2.5 Sample Spaces Having Equally Likely Outcomes 35 -- 2.6 Probability As a Continuous Set Function 47 -- 2.7 Probability As a Measure of Belief 51 -- 3 Conditional Probability and Independence 64 -- 3.2 Conditional Probabilities 64 -- 3.3 Bayes' Formula 69 -- 3.4 Independent Events 83 -- 3.5 P( -[middle dot]F) is a Probability 96 -- 4 Random Variables 122 -- 4.1 Random Variables 122 -- 4.2 Discrete Random Variables 127 -- 4.3 Expected Value 130 -- 4.4 Expectatio of a Function of a Random Variable 133 -- 4.5 Variance 137 -- 4.6 The Bernoulli and Binomial Random Variables 139 -- 4.6.1 Properties of Binomial Random Variables 144 -- 4.6.2 Computing the Binomial Distribution Function 147 -- 4.7 The Poisson Random Variable 149 -- 4.7.1 Computing the Poisson Distribution Function 157 -- 4.8 Other Discrete Probability Distribution 158 -- 4.8.1 The Geometric Random Variable 158 -- 4.8.2 The Negative Binomial Random Variable 160 -- 4.8.3 The Hypergeometric Random Variable 162 -- 4.8.4 The Zeta (or Zipf) distribution 166 -- 4.9 Properties of the Cumulative Distribution Function 166 -- 5 Continuous Random Variables 187 -- 5.2 Expectation and Variance of Continuous Random Variables 190 -- 5.3 The Uniform Random Variable 195 -- 5.4 Normal Random Variables 199 -- 5.4.1 The Normal Approximation to the Binomial Distribution 206 -- 5.5 Exponential Random Variables 210 -- 5.5.1 Hazard Rate Functions 215 -- 5.6 Other Continuous Distributions 217 -- 5.6.1 The Gamma Distribution 217 -- 5.6.2 The Weibull Distribution 220 -- 5.6.3 The Cauchy Distribution 220 -- 5.6.4 The Beta Distribution 221 -- 5.7 The Distribution of a Function of a Random Variable 223 -- 6 Jointly Distributed Random Variables 239 -- 6.1 Joint Distribution Functions 239 -- 6.2 Independent Random Variables 248 -- 6.3 Sums of Independent Random Variables 260 -- 6.4 Conditional Distributions: Discrete Case 268 -- 6.5 Conditional Distributions: Continuous Case 270 -- 6.6 Order Statistics 273 -- 6.7 Joint Probability Distribution of Functions of Random Variables 277 -- 6.8 Exchangeable Random Variables 285 -- 7 Properties of Expectation 304 -- 7.2 Expectation of Sums of Random Variables 305 -- 7.2.1 Obtaining Bounds from Expectations via the Probabilistic Method 321 -- 7.2.2 The Maximum-Minimums Identity 324 -- 7.3 Covariance, Variance of Sums, and Correlations 327 -- 7.4 Conditional Expectation 340 -- 7.4.2 Computing Expectations by Conditioning 343 -- 7.4.3 Computing Probabilities by Conditioning 350 -- 7.4.4 Conditional Variance 354 -- 7.5 Conditional Expectation and Prediction 356 -- 7.6 Moment Generating Functions 361 -- 7.6.1 Joint Moment Generating Functions 371 -- 7.7 Additional Properties of Normal Random Variables 373 -- 7.7.1 The Multivariate Normal Distribution 373 -- 7.7.2 The Joint Distribution of the Sample Mean and Sample Variance 374 -- 7.8 General Definition of Expectation 375 -- 8 Limit Theorems 400 -- 8.2 Chebyshev's Inequality and the Weak Law of Large Numbers 400 -- 8.3 The Central Limit Theorem 403 -- 8.4 The Strong Law of Large Numbers 412 -- 8.5 Other Inequalities 417 -- 8.6 Bounding the Error Probability When Approximating a Sum of Independent Bernoulli Random Variables by a Poisson 424 -- 9 Additional Topics in Probability 432 -- 9.1 The Poisson Process 432 -- 9.2 Markov Chains 435 -- 9.3 Surprise, Uncertainty, and Entropy 440 -- 9.4 Coding Theory and Entropy 445 -- 10 Simulation 455 -- 10.2 General Techniques for Simulating Continuous Random Variables 458 -- 10.2.1 The Inverse Transformation Method 458 -- 10.2.2 The Rejection Method 459 -- 10.3 Simulating from Discrete Distributions 465 -- 10.4 Variance Reduction Techniques 467 -- 10.4.1 Use of Antithetic Variables 468 -- 10.4.2 Variance Reduction by Conditioning 468 -- 10.4.3 Control Variates 470.

ISBN

0130338516

LCCN

^^2001033915

Owning Institutions

Harvard Library