A first course in probability / Sheldon Ross.

Format:

Book

Author/Creator:

Ross, Sheldon M.

Contributor:

Class of 1924 Book Fund.

Language:

English

Subjects (All):

Probabilities.

Physical Description:

viii, 520 pages ; 24 cm

Edition:

Sixth edition.

Place of Publication:

Upper Saddle River, N.J. : Prentice Hall, 2002.

Summary:

This market-leading introduction to probability features exceptionally clear explanations of the mathematics of probability theory and explores its many diverse applications through numerous interesting and motivational examples. The outstanding problem sets are a hallmark feature of this book. Provides clear, complete explanations to fully explain mathematical concepts. Features subsections on the probabilistic method and the maximum-minimums identity. Includes many new examples relating to DNA matching, utility, finance, and applications of the probabilistic method. Features an intuitive treatment of probability--intuitive explanations follow many examples. The Probability Models Disk" included with each copy of the book, contains six probability models that are referenced in the book and allow readers to quickly and easily perform calculations and simulations.

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.

Notes:

Includes index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Class of 1924 Book Fund.

ISBN:

0130338516

OCLC:

47018471