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### Summary

### Summary

Suited for a first course in applied probability and statistics for engineering or science majors, this is a superior textbook. Introduction to Probability and Statistics for Engineers and Scientists, Second Edition, includes expanded coverage of quality control, and offers unique software that automates the computations required for exercises, as well as illustrating the main concepts of probability. The author emphasizes the manner in which probability yields insight into statistical problems; ultimately resulting in an intuitive understanding of the statistical procedures most often used by practicing engineers and scientists. Real data sets are incorporated in a wide variety of exercises and examples throughout the book, and this emphasis on data motivates the probability coverage.

### Author Notes

Sheldon M. Ross has published numerous textbooks and technical articles in the areas of statistics and applied probability. Professor Ross is the founding and continuing editor of the journal Probability in the Engineering and Informational Sciences, published by Cambridge University Press. He is a fellow of the Institute of Mathematical Statistics and a recipient of the Humboldt U.S. Senior Scientist award.

### Table of Contents

Preface | p. xiii |

Chapter 1 Introduction to Statistics | p. 1 |

1.1 Introduction | p. 1 |

1.2 Data Collection and Descriptive Statistics | p. 1 |

1.3 Inferential Statistics and Probability Models | p. 2 |

1.4 Populations and Samples | p. 3 |

1.5 A Brief History of Statistics | p. 3 |

Problems | p. 7 |

Chapter 2 Descriptive Statistics | p. 9 |

2.1 Introduction | p. 9 |

2.2 Describing Data Sets | p. 9 |

2.2.1 Frequency Tables and Graphs | p. 10 |

2.2.2 Relative Frequency Tables and Graphs | p. 10 |

2.2.3 Grouped Data, Histograms, Ogives, and Stem and Leaf Plots | p. 14 |

2.3 Summarizing Data Sets | p. 19 |

2.3.1 Sample Mean, Sample Median, and Sample Mode | p. 19 |

2.3.2 Sample Variance and Sample Standard Deviation | p. 23 |

2.3.3 Sample Percentiles and Box Plots | p. 25 |

2.4 Chebyshev's Inequality | p. 29 |

2.5 Normal Data Sets | p. 30 |

2.6 Paired Data Sets and the Sample Correlation Coefficient | p. 34 |

Problems | p. 40 |

Chapter 3 Elements of Probability | p. 59 |

3.1 Introduction | p. 59 |

3.2 Sample Space and Events | p. 60 |

3.3 Venn Diagrams and the Algebra of Events | p. 62 |

3.4 Axioms of Probability | p. 63 |

3.5 Sample Spaces Having Equally Likely Outcomes | p. 65 |

3.6 Conditional Probability | p. 70 |

3.7 Bayes' Formula | p. 74 |

3.8 Independent Events | p. 79 |

Problems | p. 82 |

Chapter 4 Random Variables and Expectation | p. 89 |

4.1 Random Variables | p. 89 |

4.2 Types of Random Variables | p. 91 |

4.3 Jointly Distributed Random Variables | p. 95 |

4.3.1 Independent Random Variables | p. 100 |

4.3.2 Conditional Distributions | p. 103 |

4.4 Expectation | p. 105 |

4.5 Properties of the Expected Value | p. 110 |

4.5.1 Expected Value of Sums of Random Variables | p. 113 |

4.6 Variance | p. 116 |

4.7 Covariance and Variance of Sums of Random Variables | p. 119 |

4.8 Moment Generating Functions | p. 123 |

4.9 Chebyshev's Inequality and the Weak Law of Large Numbers | p. 124 |

Problems | p. 127 |

Chapter 5 Special Random Variables | p. 137 |

5.1 The Bernoulli and Binomial Random Variables | p. 137 |

5.1.1 Computing the Binomial Distribution Function | p. 142 |

5.2 The Poisson Random Variable | p. 144 |

5.2.1 Computing the Poisson Distribution Function | p. 150 |

5.3 The Hypergeometric Random Variable | p. 150 |

5.4 The Uniform Random Variable | p. 154 |

5.5 Normal Random Variables | p. 160 |

5.6 Exponential Random Variables | p. 167 |

5.6.1 The Poisson Process | p. 171 |

5.7 The Gamma Distribution | p. 173 |

5.8 Distributions Arising from the Normal | p. 177 |

5.8.1 The Chi-Square Distribution | p. 177 |

5.8.1.1 The Relation between Chi-Square and Gamma Random Variables | p. 178 |

5.8.2 The t-Distribution | p. 180 |

5.8.3 The F-Distribution | p. 182 |

Problems | p. 184 |

Chapter 6 Distributions of Sampling Statistics | p. 191 |

6.1 Introduction | p. 191 |

6.2 The Sample Mean | p. 192 |

6.3 The Central Limit Theorem | p. 193 |

6.3.1 Approximate Distribution of the Sample Mean | p. 200 |

6.3.2 How Large a Sample Is Needed | p. 203 |

6.4 The Sample Variance | p. 203 |

6.5 Sampling Distributions from a Normal Population | p. 204 |

6.5.1 Distribution of the Sample Mean | p. 204 |

6.5.2 Joint Distribution of X and S[superscript 2] | p. 204 |

6.6 Sampling from A Finite Population | p. 206 |

Problems | p. 210 |

Chapter 7 Parameter Estimation | p. 217 |

7.1 Introduction | p. 217 |

7.2 Maximum Likelihood Estimators | p. 218 |

7.3 Interval Estimates | p. 223 |

7.3.1 Confidence Interval for a Normal Mean When the Variance Is Unknown | p. 229 |

7.3.2 Confidence Intervals for the Variance of a Normal Distribution | p. 234 |

7.4 Estimating the Difference in Means of Two Normal Populations | p. 235 |

7.5 Approximate Confidence Interval for the Mean of a Bernoulli Random Variable | p. 242 |

7.6 Confidence Interval of the Mean of the Exponential Distribution | p. 246 |

7.7 Evaluating a Point Estimator | p. 247 |

7.8 The Bayes Estimator | p. 253 |

Problems | p. 258 |

Chapter 8 Hypothesis Testing | p. 271 |

8.1 Introduction | p. 271 |

8.2 Significance Levels | p. 272 |

8.3 Tests Concerning the Mean of a Normal Population | p. 273 |

8.3.1 Case of Known Variance | p. 273 |

8.3.1.1 One-Sided Tests | p. 279 |

8.3.2 Case of Unknown Variance: The t-Test | p. 284 |

8.4 Testing the Equality of Means of Two Normal Populations | p. 291 |

8.4.1 Case of Known Variances | p. 291 |

8.4.2 Case of Unknown Variances | p. 293 |

8.4.3 Case of Unknown and Unequal Variances | p. 297 |

8.4.4 The Paired t-Test | p. 297 |

8.5 Hypothesis Tests Concerning the Variance of a Normal Population | p. 299 |

8.5.1 Testing for the Equality of Variances of Two Normal Populations | p. 301 |

8.6 Hypothesis Tests in Bernoulli Populations | p. 302 |

8.6.1 Testing the Equality of Parameters in Two Bernoulli Populations | p. 305 |

8.6.1.1 Computations for the Fisher-Irwin Test | p. 306 |

8.7 Tests Concerning the Mean of a Poisson Distribution | p. 307 |

8.7.1 Testing the Relationship between Two Poisson Parameters | p. 308 |

Problems | p. 309 |

Chapter 9 Regression | p. 325 |

9.1 Introduction | p. 325 |

9.2 Least Squares Estimators of the Regression Parameters | p. 327 |

9.3 Distribution of the Estimators | p. 330 |

9.4 Statistical Inferences about the Regression Parameters | p. 335 |

9.4.1 Inferences Concerning [beta] | p. 335 |

9.4.1.1 Regression to the Mean | p. 339 |

9.4.2 Inferences Concerning [alpha] | p. 343 |

9.4.3 Inferences Concerning the Mean Response [alpha] + [beta]X | p. 343 |

9.4.4 Prediction Interval of a Future Response | p. 345 |

9.4.5 Summary of Distributional Results | p. 347 |

9.5 The Coefficient of Determination and the Sample Correlation Coefficient | p. 348 |

9.6 Analysis of Residuals: Assessing the Model | p. 350 |

9.7 Transforming to Linearity | p. 352 |

9.8 Weighted Least Squares | p. 356 |

9.9 Polynomial Regression | p. 362 |

9.10 Multiple Linear Regression | p. 365 |

9.10.1 Predicting Future Responses | p. 376 |

Problems | p. 381 |

Chapter 10 Analysis of Variance | p. 405 |

10.1 Introduction | p. 405 |

10.2 An Overview | p. 406 |

10.3 One-Way Analysis of Variance | p. 408 |

10.3.1 Multiple Comparisons of Sample Means | p. 414 |

10.3.2 One-Way Analysis of Variance with Unequal Sample Sizes | p. 416 |

10.4 Two-Factor Analysis of Variance: Introduction and Parameter Estimation | p. 417 |

10.5 Two-Factor Analysis of Variance: Testing Hypotheses | p. 421 |

10.6 Two-Way Analysis of Variance with Interaction | p. 425 |

Problems | p. 434 |

Chapter 11 Goodness of Fit Tests and Categorical Data Analysis | p. 447 |

11.1 Introduction | p. 447 |

11.2 Goodness of Fit Tests When All Parameters Are Specified | p. 448 |

11.2.1 Determining the Critical Region by Simulation | p. 453 |

11.3 Goodness of Fit Tests When Some Parameters Are Unspecified | p. 456 |

11.4 Tests of Independence in Contingency Tables | p. 458 |

11.5 Tests of Independence in Contingency Tables Having Fixed Marginal Totals | p. 463 |

11.6 The Kolmogorov-Smirnov Goodness of Fit Test for Continuous Data | p. 466 |

Problems | p. 470 |

Chapter 12 Nonparametric Hypothesis Tests | p. 479 |

12.1 Introduction | p. 479 |

12.2 The Sign Test | p. 479 |

12.3 The Signed Rank Test | p. 483 |

12.4 The Two-Sample Problem | p. 488 |

12.4.1 The Classical Approximation and Simulation | p. 492 |

12.5 The Runs Test for Randomness | p. 494 |

Problems | p. 499 |

Chapter 13 Quality Control | p. 507 |

13.1 Introduction | p. 507 |

13.2 Control Charts for Average Values: The X-Control Charts | p. 508 |

13.2.1 Case of Unknown [mu] and [sigma] | p. 511 |

13.3 S-Control Charts | p. 515 |

13.4 Control Charts for the Fraction Defective | p. 518 |

13.5 Control Charts for Number of Defects | p. 520 |

13.6 Other Control Charts for Detecting Changes in the Population Mean | p. 523 |

13.6.1 Moving-Average Control Charts | p. 524 |

13.6.2 Exponentially Weighted Moving-Average Control Charts | p. 526 |

13.6.3 Cumulative Sum Control Charts | p. 530 |

Problems | p. 533 |

Chapter 14 Life Testing | p. 541 |

14.1 Introduction | p. 541 |

14.2 Hazard Rate Functions | p. 541 |

14.3 The Exponential Distribution in Life Testing | p. 544 |

14.3.1 Simultaneous Testing -- Stopping at the rth Failure | p. 544 |

14.3.2 Sequential Testing | p. 549 |

14.3.3 Simultaneous Testing -- Stopping by a Fixed Time | p. 553 |

14.3.4 The Bayesian Approach | p. 555 |

14.4 A Two-Sample Problem | p. 557 |

14.5 The Weibull Distribution in Life Testing | p. 558 |

14.5.1 Parameter Estimation by Least Squares | p. 560 |

Problems | p. 562 |

Appendix of Tables | p. 569 |

Index | p. 575 |