A First Course in Probability

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9780137463145 | 0137463146
Cover: Hardcover
Copyright: 8/1/1997

Rent

(Recommended)

$75.98

Term

Due

Price

Semester

Dec 13

$79.98

Quarter

Aug 16

$75.98

Short Term

Jul 3

$71.99

*This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping cart.
Buy Used

Usually Ships in 2-4 Business Days

$71.34
Buy New

In Stock Usually Ships in 24 Hours.

$76.34

This market leader is written as an elementary introduction to the mathematical theory of probability for students in mathematics, engineering, and the sciences who possess the prerequisite knowledge of elementary calculus. A major thrust of the Fifth Edition has been to make the book more accessible to today's students. The exercise sets have been revised to include more simple, mechanical problems and a new section of Self-Test Problems with fully worked out solutions conclude each chapter. In addition, many new applications have been added to demonstrate the importance of probability in real situations. A software diskette, referenced in text and packaged with each copy of the book, provides an easy to use tool for students to derive probabilities for binomial, Poisson, and normal random variables, illustrate and explore the central limit theorem, work with the strong law of large numbers, and more.

PREFACE

1 COMBINATORIAL ANALYSIS

(24)

1.1 Introduction

(1)

1.2 The Basic Principle of Counting

(1)

1.3 Permutations

(2)

1.4 Combinations

(5)

1.5 Multinomial Coefficients

(2)

1.6 On the Distribution of Balls in Urns*

(3)

Summary

(1)

Problems

(3)

Theoretical Exercises

(4)

Self-Test Problems and Exercises

(2)

2 AXIOMS OF PROBABILITY

(42)

2.1 Introduction

(1)

2.2 Sample Space and Events

(5)

2.3 Axioms of Probability

(2)

2.4 Some Simple Propositions

(4)

2.5 Sample Spaces Having Equally Likely Outcomes

(12)

2.6 Probability As a Continuous Set Function*

(4)

2.7 Probability As a Measure of Belief

(1)

Summary

(1)

Problems

(7)

Theoretical Exercises

(3)

Self-Test Problems and Exercises

(3)

3 CONDITIONAL PROBABILITY AND INDEPENDENCE

(59)

3.1 Introduction

(1)

3.2 Conditional Probabilities

(5)

3.3 Bayes' Formula

(11)

3.4 Independent Events

(13)

3.5 P(.\F) is a Probability(*)

(7)

Summary

103

(1)

Problems

104

(14)

Theoretical Exercises

118

(5)

Self-Test Problems and Exercises

123

(3)

4 RANDOM VARIABLES

126

(66)

4.1 Random Variables

126

(5)

4.2 Distribution Functions

131

(3)

4.3 Discrete Random Variables

134

(2)

4.4 Expected Value

136

(3)

4.5 Expectation of a Function of a Random Variable

139

(3)

4.6 Variance

142

(2)

4.7 The Bernoulli and Binomial Random Variables

144

(10)

4.7.1 Properties of Binomial Random Variables

149

(3)

4.7.2 Computing the Binomial Distribution Function

152

(2)

4.8 The Poisson Random Variable

154

(8)

4.8.1 Computing the Poisson Distribution Function

161

(1)

4.9 Other Discrete Probability Distribution

162

(9)

4.9.1 The Geometric Random Variable

162

(2)

4.9.2 The Negative Binomial Random Variable

164

(3)

4.9.3 The Hypergeometric Random Variable

167

(3)

4.9.4 The Zeta (or Zipf) distribution

170

(1)

Summary

171

(2)

Problems

173

(11)

Theoretical Exercises

184

(5)

Self-Test Problems and Exercises

189

(3)

5 CONTINUOUS RANDOM VARIABLES

192

(52)

5.1 Introduction

192

(3)

5.2 Expectation and Variance of Continuous Random Variables

195

(5)

5.3 The Uniform Random Variable

200

(4)

5.4 Normal Random Variables

204

(11)

5.4.1 The Normal Approximation to the Binomial Distribution

212

(3)

5.5 Exponential Random Variables

215

(7)

5.5.1 Hazard Rate Functions

220

(2)

5.6 Other Continuous Distributions

222

(5)

5.6.1 The Gamma Distribution

222

(2)

5.6.2 The Weibull Distribution

224

(1)

5.6.3 The Cauchy Distribution

225

(1)

5.6.4 The Beta Distribution

226

(1)

5.7 The Distribution of a Function of a Random Variable

227

(3)

Summary

230

(2)

Problems

232

(5)

Theoretical Exercises

237

(4)

Self-Test Problems and Exercises

241

(3)

6 JOINTLY DISTRIBUTED RANDOM VARIABLES

244

(65)

6.1 Joint Distribution Functions

244

(8)

6.2 Independent Random Variables

252

(2)

6.3 Sums of Independent Random Variables

264

(8)

6.4 Conditional Distributions: Discrete Case

272

(1)

6.5 Conditional Distributions: Continuous Case

273

(3)

6.6 Order Statistics*

276

(4)

6.7 Joint Probability Distribution of Functions of Random Variables

280

(8)

6.8 Exchangeable Random Variables*

288

(3)

Summary

291

(2)

Problems

293

(7)

Theoretical Exercises

300

(5)

Self-Test Problem and Exercises

305

(4)

7 PROPERTIES OF EXPECTATION

309

(86)

7.1 Introduction

309

(1)

7.2 Expectation of Sums of Random Variables

310

(15)

7.3 Covariance, Variance of Sums, and Correlations

325

(10)

7.4 Conditional Expectation

335

(15)

7.4.1 Definitions

335

(2)

7.4.2 Computing Expectations by Conditioning

337

(7)

7.4.3 Computing Probabilities by Conditioning

344

(4)

7.4.4 Conditional Variance

348

(2)

7.5 Conditional Expectation and Prediction

350

(5)

7.6 Moment Generating Functions

355

(10)

7.6.1 Joint Moment Generating Functions

364

(1)

7.7 Additional Properties of Normal Random Variables

365

(3)

7.7.1 The Multivariate Normal Distribution

365

(1)

7.7.2 The Joint Distribution of the Sample Mean and Sample Variance

366

(2)

7.8 General Definition of Expectation(*)

368

(2)

Summary

370

(2)

Problems

372

(12)

Theoretical Exercises

384

(8)

Self-Test Problems and Exercises

392

(3)

8 LIMIT THEOREMS

395

(33)

8.1 Introduction

395

(1)

8.2 Chebyshev's Inequality and the Weak Law of Large Numbers

395

(4)

8.3 The Central Limit Theorem

399

(8)

8.4 The Strong Law of Large Numbers

407

(5)

8.5 Other Inequalities

412

(6)

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

418

(3)

Summary

421

(1)

Problems

421

(3)

Theoretical Exercises

424

(2)

Self-Test Problems and Exercises

426

(2)

9 ADDITIONAL TOPICS IN PROBABILITY

428

(24)

9.1 The Poisson Process

428

(3)

9.2 Markov Chains

431

(5)

9.3 Surprise, Uncertainty, and Entropy

436

(5)

9.4 Coding Theory and Entropy

441

(1)

Summary

441

(7)

Theoretical Exercises and Problems

448

(2)

Self-Test Problems and Exercises

450

(1)

References

450

(2)

10 SIMULATION

452

(21)

10.1 Introduction

452

(3)

10.2 General Techniques for Simulating Continuous Random Variables

455

(7)

10.2.1 The Inverse Transformation Method

455

(1)

10.2.2 The Rejection Method

456

(6)

10.3 Simulating from Discrete Distributions

462

(2)

10.4 Variance Reduction Techniques

464

(4)

10.4.1 Use of Antithetic Variables

465

(1)

10.4.2 Variance Reduction by Conditioning

466

(2)

10.4.3 Control Variates

468

(1)

Summary

468

(1)

Problems

469

(2)

Self-Test Problems and Exercises

472

(1)

References

472

(1)

Appendix A ANSWERS TO SELECTED PROBLEMS

473

(4)

Appendix B SOLUTIONS TO SELF-TEST PROBLEMS AND EXERCISES

477

(36)

INDEX

513

Please wait while the item is added to your bag...

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

A First Course in Probability

Summary

Table of Contents

Supplemental Materials