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First Course in Probability, A

by: Ross, Sheldon M.

First Course in Probability, A

by: Ross, Sheldon M.

ISBN 13:
9780130338518
ISBN 10:
0130338516
Edition: 6th
Format: Hardcover
Copyright: 01/01/2002
Publisher: PRENTICE HALL
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Summary

For upper level or undergraduate/graduate level introduction to probability for math, science, engineering, and business students with a background in elementary calculus. 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 and intuitive explanations are hallmark features of this market leading text.

Preface

Combinatorial Analysis

(23)

Introduction

(1)

The Basic Principle of Counting

(1)

Permutations

(2)

Combinations

(5)

Multinomial Coefficients

(2)

The Number of Integer Solutions of Equations*

(12)

Summary

(1)

Problems

(7)

Theoretical Exercises

(1)

Self-Test Problems and Exercises

(2)

Axioms of Probability

(40)

Introduction

(1)

Sample Space and Events

(4)

Axioms of Probability

(3)

Some Simple Propositions

(4)

Sample Spaces Having Equally Likely Outcomes

(12)

Probability As a Continuous Set Function*

(4)

Probability As a Measure of Belief

(13)

Summary

(1)

Problems

(6)

Theoretical Exercises

(2)

Self-Test Problems and Exercises

(3)

Conditional Probability and Independence

(58)

Introduction

(1)

Conditional Probabilities

(5)

Bayes' Formula

(14)

Independent Events

(13)

P(•/F) is a Probability*

(26)

Summary

103

(1)

Problems

104

(11)

Theoretical Exercises

115

(4)

Self-Test Problems and Exercises

119

(3)

Random Variables

122

(65)

Random Variables

122

(5)

Discrete Random Variables

127

(3)

Expected Value

130

(3)

Expectation of a Function of a Random Variable

133

(4)

Variance

137

(2)

The Bernoulli and Binomial Random Variables

139

(10)

Properties of Binomial Random Variables

144

(3)

Computing the Binomial Distribution Function

147

(2)

The Poisson Random Variable

149

(9)

Computing the Poisson Distribution Function

157

(1)

Other Discrete Probability Distribution

158

(8)

The Geometric Random Variable

158

(2)

The Negative Binomial Random Variable

160

(2)

The Hypergeometric Random Variable

162

(4)

The Zeta (or Zipf) distribution

166

(1)

Properties of the Cumulative Distribution Function

166

(21)

Summary

169

(2)

Problems

171

(9)

Theoretical Exercises

180

(4)

Self-Test Problems and Exercises

184

(3)

Continuous Random Variables

187

(52)

Introduction

187

(3)

Expectation and Variance of Continuous Random Variables

190

(5)

The Uniform Random Variable

195

(4)

Normal Random Variables

199

(11)

The Normal Approximation to the Binomial Distribution

206

(4)

Exponential Random Variables

210

(7)

Hazard Rate Functions

215

(2)

Other Continuous Distributions

217

(6)

The Gamma Distribution

217

(3)

The Weibull Distribution

220

(1)

The Cauchy Distribution

220

(1)

The Beta Distribution

221

(2)

The Distribution of a Function of a Random Variable

223

(16)

Summary

225

(3)

Problems

228

(4)

Theoretical Exercises

232

(3)

Self-Test Problems and Exercises

235

(4)

Jointly Distributed Random Variables

239

(65)

Joint Distribution Functions

239

(9)

Independent Random Variables

248

(12)

Sums of Independent Random Variables

260

(8)

Conditional Distributions: Discrete Case

268

(2)

Conditional Distributions: Continuous Case

270

(3)

Order Statistics*

273

(4)

Joint Probability Distribution of Functions of Random Variables

277

(8)

Exchangeable Random Variables*

285

(19)

Summary

288

(2)

Problems

290

(6)

Theoretical Exercises

296

(3)

Self-Test Problems and Exercises

299

(5)

Properties of Expectations

304

(96)

Introduction

304

(1)

Expectation of Sums of Random Variables

305

(22)

Obtaining Bounds from Expectations via the Probabilistic Method*

321

(3)

The Maximum-Minimums Identity*

324

(3)

Covariance, Variance of Sums, and Correlations

327

(13)

Conditional Expectation

340

(16)

Definitions

340

(3)

Computing Expectations by Conditioning

343

(7)

Computing Probabilities by Conditioning

350

(4)

Conditional Variance

354

(2)

Conditional Expectation and Prediction

356

(5)

Moment Generating Functions

361

(12)

Joint Moment Generating Functions

371

(2)

Additional Properties of Normal Random Variables

373

(2)

The Multivariate Normal Distribution

373

(1)

The Joint Distribution of the Sample Mean and Sample Variance

374

(1)

General Definition of Expectation*

375

(25)

Summary

377

(2)

Problems

379

(10)

Theoretical Exercises

389

(8)

Self-Test Problems and Exercises

397

(3)

Limit Theorems

400

(32)

Introduction

400

(1)

Chebyshev's Inequality and the Weak Law of Large Numbers

400

(3)

The Central Limit Theorem

403

(9)

The Strong Law of Large Numbers

412

(5)

Other Inequalities

417

(7)

Bounding the Error Probability When Approximating a Sum of Independent Bernoulli Random Variables by a Poisson

424

(8)

Summary

426

(1)

Problems

427

(2)

Theoretical Exercises

429

(1)

Self-Test Problems and Exercises

430

(2)

Additional Topics in Probability

432

(23)

The Poisson Process

432

(3)

Markov Chains

435

(5)

Surprise, Uncertainty, and Entropy

440

(5)

Coding Theory and Entropy

445

(10)

Summary

451

(1)

Theoretical Exercises and Problems

452

(2)

Self-Test Problems and Exercises

454

(1)

References

454

(1)

Simulation

455

(20)

Introduction

455

(3)

General Techniques for Simulating Continuous Random Variables

458

(7)

The Inverse Transformation Method

458

(1)

The Rejection Method

459

(6)

Simulating from Discrete Distributions

465

(2)

Variance Reduction Techniques

467

(8)

Use of Antithetic Variables

468

(1)

Variance Reduction by Conditioning

468

(2)

Control Variates

470

(1)

Summary

471

(1)

Problems

471

(3)

Self-Test Problems and Exercises

474

(1)

References

474

(1)

Appendix A Answers to Selected Problems

475

(3)

Appendix B Solutions to Self-Test Problems and Exercises

478

(41)

Index

519

Amazon no longer offers textbook rentals. We do!

First Course in Probability, A

First Course in Probability, A

9780130338518

0130338516

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

First Course in Probability, A

First Course in Probability, A

9780130338518

0130338516

Summary

Table of Contents

Supplemental Materials

Write a Review

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