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<p>Preface for the First Edition xi</p> <p>Preface for the Second Edition xv</p> <p><b>1. Sample Spaces and Probability 1</b></p> <p>1.1. Discrete Sample Spaces 1</p> <p>1.2. Events; Axioms of Probability 7</p> <p>Axioms of Probability 8</p> <p>1.3. Probability Theorems 10</p> <p>1.4. Conditional Probability and Independence 14</p> <p>Independence 23</p> <p>1.5. Some Examples 28</p> <p>1.6. Reliability of Systems 34</p> <p>Series Systems 34</p> <p>Parallel Systems 35</p> <p>1.7. Counting Techniques 39</p> <p>Chapter Review 54</p> <p>Problems for Review 56</p> <p>Supplementary Exercises for Chapter 1 56</p> <p><b>2. Discrete Random Variables and Probability Distributions 61</b></p> <p>2.1. Random Variables 61</p> <p>2.2. Distribution Functions 68</p> <p>2.3. Expected Values of Discrete Random Variables 72</p> <p>Expected Value of a Discrete Random Variable 72</p> <p>Variance of a Random Variable 75</p> <p>Tchebycheff’s Inequality 78</p> <p>2.4. Binomial Distribution 81</p> <p>2.5. A Recursion 82</p> <p>The Mean and Variance of the Binomial 84</p> <p>2.6. Some Statistical Considerations 88</p> <p>2.7. Hypothesis Testing: Binomial Random Variables 92</p> <p>2.8. Distribution of A Sample Proportion 98</p> <p>2.9. Geometric and Negative Binomial Distributions 102</p> <p>A Recursion 108</p> <p>2.10. The Hypergeometric Random Variable: Acceptance Sampling 111</p> <p>Acceptance Sampling 111</p> <p>The Hypergeometric Random Variable 114</p> <p>Some Specific Hypergeometric Distributions 116</p> <p>2.11. Acceptance Sampling (Continued) 119</p> <p>Producer’s and Consumer’s Risks 121</p> <p>Average Outgoing Quality 122</p> <p>Double Sampling 124</p> <p>2.12. The Hypergeometric Random Variable: Further Examples 128</p> <p>2.13. The Poisson Random Variable 130</p> <p>Mean and Variance of the Poisson 131</p> <p>Some Comparisons 132</p> <p>2.14. The Poisson Process 134</p> <p>Chapter Review 139</p> <p>Problems for Review 141</p> <p>Supplementary Exercises for Chapter 2 142</p> <p><b>3. Continuous Random Variables and Probability Distributions 146</b></p> <p>3.1. Introduction 146</p> <p>Mean and Variance 150</p> <p>A Word on Words 153</p> <p>3.2. Uniform Distribution 157</p> <p>3.3. Exponential Distribution 159</p> <p>Mean and Variance 160</p> <p>Distribution Function 161</p> <p>3.4. Reliability 162</p> <p>Hazard Rate 163</p> <p>3.5. Normal Distribution 166</p> <p>3.6. Normal Approximation to the Binomial Distribution 175</p> <p>3.7. Gamma and Chi-Squared Distributions 178</p> <p>3.8. Weibull Distribution 184</p> <p>Chapter Review 186</p> <p>Problems For Review 189</p> <p>Supplementary Exercises for Chapter 3 189</p> <p><b>4. Functions of Random Variables; Generating Functions; Statistical Applications 194</b></p> <p>4.1. Introduction 194</p> <p>4.2. Some Examples of Functions of Random Variables 195</p> <p>4.3. Probability Distributions of Functions of Random Variables 196</p> <p>Expectation of a Function of X 199</p> <p>4.4. Sums of Random Variables I 203</p> <p>4.5. Generating Functions 207</p> <p>4.6. Some Properties of Generating Functions 211</p> <p>4.7. Probability Generating Functions for Some Specific Probability Distributions 213</p> <p>Binomial Distribution 213</p> <p>Poisson’s Trials 214</p> <p>Geometric Distribution 215</p> <p>Collecting Premiums in Cereal Boxes 216</p> <p>4.8. Moment Generating Functions 218</p> <p>4.9. Properties of Moment Generating Functions 223</p> <p>4.10. Sums of Random Variables–II 224</p> <p>4.11. The Central Limit Theorem 229</p> <p>4.12. Weak Law of Large Numbers 233</p> <p>4.13. Sampling Distribution of the Sample Variance 234</p> <p>4.14. Hypothesis Tests and Confidence Intervals for a Single Mean 240</p> <p>Confidence Intervals, 𝜎 Known 241</p> <p>Student’s t Distribution 242</p> <p>p Values 243</p> <p>4.15. Hypothesis Tests on Two Samples 248</p> <p>Tests on Two Means 248</p> <p>Tests on Two Variances 251</p> <p>4.16. Least Squares Linear Regression 258</p> <p>4.17. Quality Control Chart for X 266</p> <p>Chapter Review 271</p> <p>Problems for Review 275</p> <p>Supplementary Exercises for Chapter 4 275</p> <p><b>5. Bivariate Probability Distributions 283</b></p> <p>5.1. Introduction 283</p> <p>5.2. Joint and Marginal Distributions 283</p> <p>5.3. Conditional Distributions and Densities 293</p> <p>5.4. Expected Values and the Correlation Coefficient 298</p> <p>5.5. Conditional Expectations 303</p> <p>5.6. Bivariate Normal Densities 308</p> <p>Contour Plots 310</p> <p>5.7. Functions of Random Variables 312</p> <p>Chapter Review 316</p> <p>Problems for Review 317</p> <p>Supplementary Exercises for Chapter 5 317</p> <p><b>6. Recursions and Markov Chains 322</b></p> <p>6.1. Introduction 322</p> <p>6.2. Some Recursions and their Solutions 322</p> <p>Solution of the Recursion (6.3) 326</p> <p>Mean and Variance 329</p> <p>6.3. Random Walk and Ruin 334</p> <p>Expected Duration of the Game 337</p> <p>6.4. Waiting Times for Patterns in Bernoulli Trials 339</p> <p>Generating Functions 341</p> <p>Average Waiting Times 342</p> <p>Means and Variances by Generating Functions 343</p> <p>6.5. Markov Chains 344</p> <p>Chapter Review 354</p> <p>Problems for Review 355</p> <p>Supplementary Exercises for Chapter 6 355</p> <p><b>7. Some Challenging Problems 357</b></p> <p>7.1. My Socks and √𝜋 357</p> <p>7.2. Expected Value 359</p> <p>7.3. Variance 361</p> <p>7.4. Other “Socks” Problems 362</p> <p>7.5. Coupon Collection and Related Problems 362</p> <p>Three Prizes 363</p> <p>Permutations 363</p> <p>An Alternative Approach 363</p> <p>Altering the Probabilities 364</p> <p>A General Result 364</p> <p>Expectations and Variances 366</p> <p>Geometric Distribution 366</p> <p>Variances 367</p> <p>Waiting for Each of the Integers 367</p> <p>Conditional Expectations 368</p> <p>Other Expected Values 369</p> <p>Waiting for All the Sums on Two Dice 370</p> <p>7.6. Conclusion 372</p> <p>7.7. Jackknifed Regression and the Bootstrap 372</p> <p>Jackknifed Regression 372</p> <p>7.8. Cook’s Distance 374</p> <p>7.9. The Bootstrap 375</p> <p>7.10. On Waldegrave’s Problem 378</p> <p>Three Players 378</p> <p>7.11. Probabilities of Winning 378</p> <p>7.12. More than Three Players 379</p> <p>r + 1 Players 381</p> <p>Probabilities of Each Player 382</p> <p>Expected Length of the Series 383</p> <p>Fibonacci Series 383</p> <p>7.13. Conclusion 384</p> <p>7.14. On Huygen’s First Problem 384</p> <p>7.15. Changing the Sums for the Players 384</p> <p>Decimal Equivalents 386</p> <p>Another Order 387</p> <p>Bernoulli’s Sequence 387</p> <p>Bibliography 388</p> <p>Appendix A. Use of Mathematica in Probability and Statistics 390</p> <p>Appendix B. Answers for Odd-Numbered Exercises 429</p> <p>Appendix C. Standard Normal Distribution 453</p> <p>Index 461</p>

<p><b>John J. Kinney, PhD,</b> is Professor Emeritus of Mathematics at Rose-Hulman Institute of Technology in Terre Haute, Indiana. A Member of the American Statistical Association and the Colorado Council of Teachers of Mathematics, Dr. Kinney is the author of numerous journal articles and three books, including <i>A Probability and Statistics Companion</i>, also published by Wiley.</p>

<p>Praise for the <i>First Edition<br /> <br /> </i>"This is a well-written and impressively presented introduction to probability and statistics. The text throughout is highly readable, and the author makes liberal use of graphs and diagrams to clarify the theory."  - <i>The Statistician<br /> <br /> </i>Thoroughly updated, <i>Probability: An Introduction with Statistical Applications, Second Edition</i> features a comprehensive exploration of statistical data analysis as an application of probability. The new edition provides an introduction to statistics with accessible coverage of reliability, acceptance sampling, confidence intervals, hypothesis testing, and simple linear regression. Encouraging readers to develop a deeper intuitive understanding of probability, the author presents illustrative geometrical presentations and arguments without the need for rigorous mathematical proofs.<br /> <br /> The <i>Second Edition</i> features interesting and practical examples from a variety of engineering and scientific fields, as well as:<br /> <br /> </p> <ul> <li>Over 880 problems at varying degrees of difficulty allowing readers to take on more challenging problems as their skill levels increase</li> </ul> <ul> <li>Chapter-by-chapter projects that aid in the visualization of probability distributions</li> </ul> <ul> <li>New coverage of statistical quality control and quality production</li> </ul> <ul> <li>An appendix dedicated to the use of Mathematica^® and a companion website containing the referenced data sets</li> </ul> <br /> Featuring a practical and real-world approach, this textbook is ideal for a first course in probability for students majoring in statistics, engineering, business, psychology, operations research, and mathematics. <i>Probability: An Introduction with Statistical Applications, Second Edition</i> is also an excellent reference for researchers and professionals in any discipline who need to make decisions based on data as well as readers interested in learning how to accomplish effective decision making from data.<br /> <br /> <b>John J. Kinney, PhD,</b> is Professor Emeritus of Mathematics at Rose-Hulman Institute of Technology in Terre Haute, Indiana. A Member of the American Statistical Association, Dr. Kinney is the author of numerous journal articles and three books, including <i>A Probability and Statistics Companion</i>, also published by Wiley.

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