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<p>Preface xi</p> <p><b>1 The Concept of Probability 1</b></p> <p>1.1 Chance Experiments – Sample Spaces 2</p> <p>1.2 Operations Between Events 11</p> <p>1.3 Probability as Relative Frequency 27</p> <p>1.4 Axiomatic Definition of Probability 38</p> <p>1.5 Properties of Probability 45</p> <p>1.6 The Continuity Property of Probability 54</p> <p>1.7 Basic Concepts and Formulas 60</p> <p>1.8 Computational Exercises 61</p> <p>1.9 Self-assessment Exercises 63</p> <p>1.9.1 True–False Questions 63</p> <p>1.9.2 Multiple Choice Questions 64</p> <p>1.10 Review Problems 67</p> <p>1.11 Applications 71</p> <p>1.11.1 System Reliability 71</p> <p>Key Terms 77</p> <p><b>2 Finite Sample Spaces – Combinatorial Methods 79</b></p> <p>2.1 Finite Sample Spaces with Events of Equal Probability 80</p> <p>2.2 Main Principles of Counting 89</p> <p>2.3 Permutations 96</p> <p>2.4 Combinations 105</p> <p>2.5 The Binomial Theorem 123</p> <p>2.6 Basic Concepts and Formulas 132</p> <p>2.7 Computational Exercises 133</p> <p>2.8 Self-Assessment Exercises 139</p> <p>2.8.1 True–False Questions 139</p> <p>2.8.2 Multiple Choice Questions 140</p> <p>2.9 Review Problems 143</p> <p>2.10 Applications 150</p> <p>2.10.1 Estimation of Population Size: Capture–Recapture Method 150</p> <p>Key Terms 152</p> <p><b>3 Conditional Probability – Independent Events 153</b></p> <p>3.1 Conditional Probability 154</p> <p>3.2 The Multiplicative Law of Probability 166</p> <p>3.3 The Law of Total Probability 174</p> <p>3.4 Bayes’ Formula 183</p> <p>3.5 Independent Events 189</p> <p>3.6 Basic Concepts and Formulas 206</p> <p>3.7 Computational Exercises 207</p> <p>3.8 Self-assessment Exercises 210</p> <p>3.8.1 True–False Questions 210</p> <p>3.8.2 Multiple Choice Questions 211</p> <p>3.9 Review Problems 214</p> <p>3.10 Applications 220</p> <p>3.10.1 Diagnostic and Screening Tests 220</p> <p>Key Terms 223</p> <p><b>4 Discrete Random Variables and Distributions 225</b></p> <p>4.1 Random Variables 226</p> <p>4.2 Distribution Functions 232</p> <p>4.3 Discrete Random Variables 247</p> <p>4.4 Expectation of a Discrete Random Variable 261</p> <p>4.5 Variance of a Discrete Random Variable 281</p> <p>4.6 Some Results for Expectation and Variance 293</p> <p>4.7 Basic Concepts and Formulas 302</p> <p>4.8 Computational Exercises 303</p> <p>4.9 Self-Assessment Exercises 309</p> <p>4.9.1 True–False Questions 309</p> <p>4.9.2 Multiple Choice Questions 310</p> <p>4.10 Review Problems 313</p> <p>4.11 Applications 317</p> <p>4.11.1 Decision Making Under Uncertainty 317</p> <p>Key Terms 320</p> <p><b>5 Some Important Discrete Distributions 321</b></p> <p>5.1 Bernoulli Trials and Binomial Distribution 322</p> <p>5.2 Geometric and Negative Binomial Distributions 337</p> <p>5.3 The Hypergeometric Distribution 358</p> <p>5.4 The Poisson Distribution 371</p> <p>5.5 The Poisson Process 385</p> <p>5.6 Basic Concepts and Formulas 394</p> <p>5.7 Computational Exercises 395</p> <p>5.8 Self-Assessment Exercises 399</p> <p>5.8.1 True–False Questions 399</p> <p>5.8.2 Multiple Choice Questions 401</p> <p>5.9 Review Problems 403</p> <p>5.10 Applications 411</p> <p>5.10.1 Overbooking 411</p> <p>Key Terms 414</p> <p><b>6 Continuous Random Variables 415</b></p> <p>6.1 Density Functions 416</p> <p>6.2 Distribution for a Function of a Random Variable 431</p> <p>6.3 Expectation and Variance 442</p> <p>6.4 Additional Useful Results for the Expectation 451</p> <p>6.5 Mixed Distributions 459</p> <p>6.6 Basic Concepts and Formulas 468</p> <p>6.7 Computational Exercises 469</p> <p>6.8 Self-Assessment Exercises 474</p> <p>6.8.1 True–False Questions 474</p> <p>6.8.2 Multiple Choice Questions 476</p> <p>6.9 Review Problems 479</p> <p>6.10 Applications 486</p> <p>6.10.1 Profit Maximization 486</p> <p>Key Terms 490</p> <p><b>7 Some Important Continuous Distributions 491</b></p> <p>7.1 The Uniform Distribution 492</p> <p>7.2 The Normal Distribution 501</p> <p>7.3 The Exponential Distribution 531</p> <p>7.4 Other Continuous Distributions 542</p> <p>7.4.1 The Gamma Distribution 543</p> <p>7.4.2 The Beta Distribution 548</p> <p>7.5 Basic Concepts and Formulas 555</p> <p>7.6 Computational Exercises 557</p> <p>7.7 Self-Assessment Exercises 561</p> <p>7.7.1 True–False Questions 561</p> <p>7.7.2 Multiple Choice Questions 562</p> <p>7.8 Review Problems 565</p> <p>7.9 Applications 573</p> <p>7.9.1 Transforming Data: The Lognormal Distribution 573</p> <p>Key Terms 578</p> <p>Appendix A Sums and Products 579</p> <p>Appendix B Distribution Function of the Standard Normal Distribution 593</p> <p>Appendix C Simulation 595</p> <p>Appendix D Discrete and Continuous Distributions 599</p> <p>Bibliography 603</p> <p>Index 605</p>

<p><b>N. Balakrishnan, PhD,</b> is a Distinguished University Professor in the Department of Mathematics and Statistics at McMaster University in Ontario, Canada. He is the author of over twenty Wiley books and served as co-editor of the Wiley's <i>Encyclopedia of Statistical Sciences, Second Edition.</i> <p><b>Markos V. Koutras, PhD,</b> is Professor in the Department of Statistics and Insurance Science at the University of Piraeus, Greece. <p><b>Konstadinos G. Politis, PhD,</b> is Associate Professor in the Department of Statistics and Insurance Science at the University of Piraeus, Greece.

<p><b>An essential guide to the concepts of probability theory that puts the focus on models and applications</b> <p><i>Introduction to Probability</i> offers an authoritative text that presents the main ideas and concepts, as well as the theoretical background, models, and applications of probability. The authors—noted experts in the field—include a review of problems where probabilistic models naturally arise, and discuss the methodology to tackle these problems. <p>A wide-range of topics are covered that include the concepts of probability and conditional probability, univariate discrete distributions, univariate continuous distributions, along with a detailed presentation of the most important probability distributions used in practice, with their main properties and applications. <p>Designed as a useful guide, the text contains theory of probability, definitions, charts, examples with solutions, illustrations, self-assessment exercises, computational exercises, problems and a glossary. This important text: <ul> <li>Includes classroom-tested problems and solutions to probability exercises</li> <li>Highlights real-world exercises designed to make clear the concepts presented</li> <li>Uses Mathematica software to illustrate the text's computer exercises</li> <li>Features applications representing worldwide situations and processes</li> <li>Offers two types of self-assessment exercises at the end of each chapter, so that students may review the material in that chapter and monitor their progress.</li> </ul> <p>Written for students majoring in statistics, engineering, operations research, computer science, physics, and mathematics, <i>Introduction to Probability: Models and Applications</i> is an accessible text that explores the basic concepts of probability and includes detailed information on models and applications.

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