Probability and Statistics for Engineers and Scientists. Anthony Hayter

PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS, Fourth Edition, continues the approach that has made previous editions successful. As a teacher and researcher at a premier engineering school, author Tony Hayter is in touch with engineers daily—and understands their vocabulary. The result of this familiarity with the professional community is a clear and readable writing style that readers understand and appreciate, as well as high-interest, relevant examples and data sets that hold readers' attention. A flexible approach to the use of computer tools includes tips for using various software packages as well as computer output (using MINITAB and other programs) that offers practice in interpreting output. Extensive use of examples and data sets illustrates the importance of statistical data collection and analysis for students in a variety of engineering areas as well as for students in physics, chemistry, computing, biology, management, and mathematics. Cover......Page 1 Title Page......Page 5 Copyright......Page 6 ABOUT THE AUTHOR......Page 7 Contents......Page 9 Preface......Page 12 Continuing Case Studies: Microelectronic Solder Joints and Internet Marketing......Page 17 1.1.2 Sample Spaces......Page 23 1.1.3 Probability Values......Page 26 1.2.1 Events and Complements......Page 30 1.2.2 Examples of Events......Page 32 1.2.3 Problems......Page 36 1.3.1 Intersections of Events......Page 37 1.3.2 Unions of Events......Page 40 1.3.3 Examples of Intersections and Unions......Page 43 1.3.4 Combinations of Three or More Events......Page 50 1.3.5 Problems......Page 53 1.4.1 Definition of Conditional Probability......Page 55 1.4.2 Examples of Conditional Probabilities......Page 56 1.5.1 General Multiplication Law......Page 62 1.5.2 Independent Events......Page 63 1.5.3 Examples and Probability Trees......Page 65 1.5.4 Problems......Page 70 1.6.1 Law of Total Probability......Page 72 1.6.2 Calculation of Posterior Probabilities......Page 73 1.6.3 Examples of Posterior Probabilities......Page 74 1.6.4 Problems......Page 77 1.7.1 Multiplication Rule......Page 78 1.7.2 Permutations and Combinations......Page 81 1.7.3 Problems......Page 85 1.8 Case Study: Microelectronic Solder Joints......Page 86 1.10 Supplementary Problems......Page 88 2.1.1 Definition of a Random Variable......Page 93 2.1.2 Probability Mass Function......Page 96 2.1.3 Cumulative Distribution Function......Page 99 2.1.4 Problems......Page 102 2.2.1 Examples of Continuous Random Variables......Page 103 2.2.2 Probability Density Function......Page 105 2.2.3 Cumulative Distribution Function......Page 109 2.2.4 Problems......Page 113 2.3.1 Expectations of Discrete Random Variables......Page 115 2.3.2 Expectations of Continuous Random Variables......Page 118 2.3.3 Medians of Random Variables......Page 121 2.3.4 Problems......Page 123 2.4.1 Definition and Interpretation of Variance......Page 124 2.4.2 Examples of Variance Calculations......Page 126 2.4.3 Chebyshevs Inequality......Page 129 2.4.4 Quantiles of Random Variables......Page 131 2.4.5 Problems......Page 135 2.5.1 Joint Probability Distributions......Page 136 2.5.2 Marginal Probability Distributions......Page 139 2.5.3 Conditional Probability Distributions......Page 142 2.5.4 Independence and Covariance......Page 145 2.5.5 Problems......Page 149 2.6.1 Linear Functions of a Random Variable......Page 151 2.6.2 Linear Combinations of Random Variables......Page 154 2.6.3 Nonlinear Functions of a Random Variable......Page 159 2.6.4 Problems......Page 162 2.7 Case Study: Microelectronic Solder Joints......Page 164 2.9 Supplementary Problems......Page 165 3.1.1 Bernoulli Random Variables......Page 169 3.1.2 Definition of the Binomial Distribution......Page 170 3.1.3 Examples of the Binomial Distribution......Page 175 3.1.4 Problems......Page 181 3.2.1 Definition of the Geometric Distribution......Page 182 3.2.2 Definition of the Negative Binomial Distribution......Page 184 3.2.3 Examples of the Geometric and Negative Binomial Distributions......Page 186 3.2.4 Problems......Page 189 3.3.1 Definition of the Hypergeometric Distribution......Page 190 3.3.2 Examples of the Hypergeometric Distribution......Page 192 3.3.3 Problems......Page 194 3.4.1 Definition of the Poisson Distribution......Page 195 3.4.2 Examples of the Poisson Distribution......Page 198 3.5.2 Examples of the Multinomial Distribution......Page 201 3.5.3 Problems......Page 204 3.6 Case Study: Microelectronic Solder Joints......Page 205 3.8 Supplementary Problems......Page 206 4.1.1 Definition of the Uniform Distribution......Page 208 4.1.2 Examples of the Uniform Distribution......Page 210 4.1.3 Problems......Page 211 4.2.1 Definition of the Exponential Distribution......Page 212 4.2.2 The Memoryless Property of the Exponential Distribution......Page 214 4.2.3 The Poisson Process......Page 215 4.2.4 Examples of the Exponential Distribution......Page 216 4.2.5 Problems......Page 220 4.3.1 Definition of the Gamma Distribution......Page 221 4.3.2 Examples of the Gamma Distribution......Page 224 4.3.3 Problems......Page 225 4.4.1 Definition of the Weibull Distribution......Page 226 4.4.2 Examples of the Weibull Distribution......Page 228 4.4.3 Problems......Page 230 4.5.2 Examples of the Beta Distribution......Page 231 4.5.3 Problems......Page 234 4.7 Case Study: Internet Marketing......Page 235 4.8 Supplementary Problems......Page 236 5.1.1 Definition of the Normal Distribution......Page 238 5.1.2 The Standard Normal Distribution......Page 239 5.1.3 Probability Calculations for General Normal Distributions......Page 244 5.1.4 Examples of the Normal Distribution......Page 247 5.1.5 Problems......Page 250 5.2.1 The Distribution of Linear Combinations of Normal Random Variables......Page 251 5.2.2 Examples of Linear Combinations of Normal Random Variables......Page 254 5.2.3 Problems......Page 260 5.3.1 The Normal Approximation to the Binomial Distribution......Page 262 5.3.2 The Central Limit Theorem......Page 265 5.3.3 Simulation Experiment 1: An Investigation of the Central Limit Theorem......Page 267 5.3.4 Examples of Employing Normal Approximations......Page 269 5.3.5 Problems......Page 272 5.4.1 The Lognormal Distribution......Page 273 5.4.2 The Chi-Square Distribution......Page 275 5.4.3 The t-distribution......Page 277 5.4.4 The F-distribution......Page 279 5.4.5 The Multivariate Normal Distribution......Page 280 5.4.6 Problems......Page 283 5.5 Case Study: Microelectronic Solder Joints......Page 284 5.7 Supplementary Problems......Page 285 6.1.1 Samples......Page 289 6.1.2 Examples......Page 291 6.1.3 Problems......Page 293 6.2.1 Bar Charts and Pareto Charts......Page 294 6.2.2 Pie Charts......Page 296 6.2.3 Histograms......Page 297 6.2.4 Outliers......Page 300 6.3 Sample Statistics......Page 302 6.3.2 Sample Median......Page 303 6.3.5 Sample Variance......Page 304 6.3.7 Boxplots......Page 306 6.3.8 Coefficient of Variation......Page 307 6.3.9 Examples......Page 308 6.3.10 Problems......Page 309 6.4 Examples......Page 310 6.5 Case Study: Microelectronic Solder Joints......Page 314 6.7 Supplementary Problems......Page 315 7.1.1 Parameters......Page 318 7.1.2 Statistics......Page 319 7.1.3 Estimation......Page 320 7.2.1 Unbiased Estimates......Page 323 7.2.2 Minimum Variance Estimates......Page 327 7.2.3 Problems......Page 332 7.3.1 Sample Proportion......Page 333 7.3.2 Sample Mean......Page 334 7.3.4 Simulation Experiment 2: An Investigation of Sampling Distributions......Page 338 7.3.5 Problems......Page 340 7.4 Constructing Parameter Estimates......Page 342 7.4.2 Maximum Likelihood Estimates......Page 344 7.4.3 Examples......Page 346 7.4.4 Problems......Page 348 7.7 Supplementary Problems......Page 349 Guide to Statistical Inference Methodologies......Page 353 8.1.1 Confidence Interval Construction......Page 355 8.1.2 Effect of the Sample Size on Confidence Intervals......Page 360 8.1.3 Further Examples......Page 362 8.1.4 Simulation Experiment 3: An Investigation of Confidence Intervals......Page 363 8.1.5 One-Sided Confidence Intervals......Page 364 8.1.6 z-Intervals......Page 367 8.1.7 Problems......Page 369 8.2.1 Hypotheses......Page 371 8.2.2 Interpretation of p-Values......Page 372 8.2.3 Calculation of p-Values......Page 375 8.2.4 Significance Levels......Page 387 8.2.5 z-Tests......Page 397 8.2.6 Problems......Page 400 8.3 Summary......Page 403 8.4 Case Study: Microelectronic Solder Joints......Page 405 8.6 Supplementary Problems......Page 406 9.1.1 Two-Sample Problems......Page 411 9.1.2 Paired Samples versus Independent Samples......Page 416 9.2.1 Methodology......Page 419 9.2.2 Examples......Page 420 9.2.3 Problems......Page 422 9.3 Analysis of Independent Samples......Page 424 9.3.1 General Procedure......Page 425 9.3.2 Pooled Variance Procedure......Page 429 9.3.3 z-Procedure......Page 432 9.3.4 Examples......Page 433 9.3.5 Sample Size Calculations......Page 440 9.3.6 Problems......Page 441 9.4 Summary......Page 444 9.5 Case Study: Microelectronic Solder Joints......Page 446 9.6 Case Study: Internet Marketing......Page 448 9.7 Supplementary Problems......Page 449 10.1 Inferences on a Population Proportion......Page 454 10.1.1 Confidence Intervals for Population Proportions......Page 456 10.1.2 Hypothesis Tests on a Population Proportion......Page 461 10.1.3 Sample Size Calculations......Page 471 10.1.4 Problems......Page 475 10.2 Comparing Two Population Proportions......Page 477 10.2.1 Confidence Intervals for the Difference between Two Population Proportions......Page 478 10.2.2 Hypothesis Tests on the Difference between Two Population Proportions......Page 482 10.2.3 Problems......Page 487 10.3 Goodness of Fit Tests for One-Way Contingency Tables......Page 488 10.3.1 One-Way Classifications......Page 489 10.3.2 Testing Distributional Assumptions......Page 496 10.3.3 Problems......Page 498 10.4.1 Two-Way Classifications......Page 500 10.4.2 Testing for Independence......Page 502 10.4.3 Problems......Page 509 10.5 Case Study: Microelectronic Solder Joints......Page 510 10.6 Case Study: Internet Marketing......Page 511 10.7 Supplementary Problems......Page 512 11.1.1 One-Factor Layouts......Page 516 11.1.2 Partitioning the Total Sum of Squares......Page 521 11.1.3 The Analysis of Variance Table......Page 529 11.1.4 Pairwise Comparisons of the Factor Level Means......Page 533 11.1.5 Sample Size Determination......Page 537 11.1.7 Problems......Page 538 11.2.1 One-Factor Layouts with Blocks......Page 542 11.2.2 Partitioning the Total Sum of Squares......Page 547 11.2.3 The Analysis of Variance Table......Page 551 11.2.4 Pairwise Comparisons of the Factor Level Means......Page 555 11.2.6 Problems......Page 557 11.3 Case Study: Microelectronic Solder Joints......Page 559 11.4 Case Study: Internet Marketing......Page 561 11.5 Supplementary Problems......Page 562 12.1.1 Model Definition and Assumptions......Page 565 12.1.2 Examples......Page 568 12.2.1 Parameter Estimation......Page 573 12.2.2 Examples......Page 577 12.2.3 Problems......Page 582 12.3.1 Inference Procedures......Page 583 12.3.2 Examples......Page 587 12.3.3 Problems......Page 590 12.4.1 Inference Procedures......Page 591 12.4.2 Examples......Page 593 12.4.3 Problems......Page 596 12.5.1 Inference Procedures......Page 597 12.5.2 Examples......Page 598 12.5.3 Problems......Page 600 12.6.1 Sum of Squares Decomposition......Page 601 12.6.3 Problems......Page 606 12.7.1 Residual Analysis Methods......Page 607 12.7.2 Examples......Page 610 12.7.3 Problems......Page 611 12.8.1 Intrinsically Linear Models......Page 612 12.9.1 The Sample Correlation Coefficient......Page 616 12.9.2 Examples......Page 620 12.9.3 Problems......Page 621 12.10 Case Study: Microelectronic Solder Joints......Page 622 12.11 Case Study: Internet Marketing......Page 623 12.12 Supplementary Problems......Page 624 13.1.1 The Multiple Linear Regression Model......Page 630 13.1.2 Fitting the Linear Regression Model......Page 632 13.1.3 Analysis of the Fitted Model......Page 634 13.1.4 Inferences on the Response Variable......Page 637 13.1.5 Problems......Page 638 13.2.1 Examples......Page 640 13.2.2 Problems......Page 649 13.3.1 Matrix Representation......Page 650 13.3.2 Problems......Page 658 13.4.1 Multicolinearity of the Input Variables......Page 659 13.4.2 Residual Analysis......Page 660 13.4.3 Influential Points......Page 662 13.5.1 Introduction......Page 665 13.5.2 Example......Page 666 13.6 Case Study: Internet Marketing......Page 669 13.7 Supplementary Problems......Page 670 14.1.1 Two-Factor Experimental Designs......Page 672 14.1.2 Models for Two-Factor Experiments......Page 675 14.1.3 Analysis of Variance Table......Page 683 14.1.4 Pairwise Comparisons of the Factor Level Means......Page 692 14.1.5 Modeling Procedures and Residual Analysis......Page 695 14.2 Experiments with Three or More Factors......Page 701 14.2.1 Three-Factor Experiments......Page 702 14.2.2 2k Experiments......Page 709 14.2.3 Problems......Page 712 14.3 Case Study: Internet Marketing......Page 714 14.4 Supplementary Problems......Page 715 CHAPTER 15 NONPARAMETRIC STATISTICAL ANALYSIS......Page 716 15.1.1 The Distribution Function......Page 717 15.1.2 The Sign Test......Page 724 15.1.3 The Signed Rank Test......Page 731 15.1.4 Problems......Page 737 15.2 Comparing Two Populations......Page 738 15.2.1 The Kolmogorov-Smirnov Test......Page 739 15.2.2 The Rank Sum Test......Page 743 15.2.3 Problems......Page 747 15.3.1 One-Way Layouts......Page 748 15.3.2 Randomized Block Designs......Page 751 15.3.3 Problems......Page 753 15.4 Case Study: Internet Marketing......Page 754 15.5 Supplementary Problems......Page 755 16.2.1 Control Charts......Page 758 16.2.2 Control Limits......Page 760 16.2.3 Properties of Control Charts......Page 762 16.3 Variable Control Charts......Page 764 16.3.1 X-Charts......Page 765 16.3.2 R-Charts......Page 766 16.3.4 Examples......Page 767 16.3.5 Problems......Page 773 16.4.1 p-Charts......Page 774 16.4.2 c-Charts......Page 777 16.4.3 Problems......Page 779 16.5.2 Acceptance Sampling Procedures......Page 780 16.6 Case Study: Internet Marketing......Page 785 16.7 Supplementary Problems......Page 786 17.1 System Reliability......Page 788 17.1.1 Components in Series......Page 789 17.1.2 Components in Parallel......Page 790 17.1.3 Complex Systems......Page 791 17.1.4 Problems......Page 793 17.2.1 Time to Failure......Page 794 17.2.2 The Hazard Rate......Page 796 17.2.3 Problems......Page 798 17.3.1 Model Fitting......Page 799 17.3.2 Censored Data......Page 802 17.4 Case Study: Internet Marketing......Page 807 17.5 Supplementary Problems......Page 808 Tables......Page 809 Answers to Odd-Numbered Problems......Page 818 Index......Page 840 Machine generated contents note: 1.1.Probabilities 1.2.Events 1.3.Combinations of Events 1.4.Conditional Probability 1.5.Probabilities of Event Intersections 1.6.Posterior Probabilities 1.7.Counting Techniques 1.8.Case Study: Microelectronic Solder Joints 1.9.Case Study: Internet Marketing 1.10.Supplementary Problems 2.1.Discrete Random Variables 2.2.Continuous Random Variables 2.3.The Expectation of a Random Variable 2.4.The Variance of a Random Variable 2.5.Jointly Distributed Random Variables 2.6.Combinations and Functions of Random Variables 2.7.Case Study: Microelectronic Solder Joints 2.8.Case Study: Internet Marketing 2.9.Supplementary Problems 3.1.The Binomial Distribution 3.2.The Geometric and Negative Binomial Distributions 3.3.The Hypergeometric Distribution 3.4.The Poisson Distribution 3.5.The Multinomial Distribution 3.6.Case Study: Microelectronic Solder Joints 3.7.Case Study: Internet Marketing 3.8.Supplementary Problems 4.1.The Uniform Distribution 4.2.The Exponential Distribution 4.3.The Gamma Distribution 4.4.The Weibull Distribution 4.5.The Beta Distribution 4.6.Case Study: Microelectronic Solder Joints 4.7.Case Study: Internet Marketing 4.8.Supplementary Problems 5.1.Probability Calculations Using the Normal Distribution 5.2.Linear Combinations of Normal Random Variables 5.3.Approximating Distributions with the Normal Distribution 5.4.Distributions Related to the Normal Distribution 5.5.Case Study: Microelectronic Solder Joints 5.6.Case Study: Internet Marketing 5.7.Supplementary Problems 6.1.Experimentation 6.2.Data Presentation 6.3.Sample Statistics 6.4.Examples 6.5.Case Study: Microelectronic Solder Joints 6.6.Case Study: Internet Marketing 6.7.Supplementary Problems 7.1.Point Estimates 7.2.Properties of Point Estimates 7.3.Sampling Distributions 7.4.Constructing Parameter Esti.