Probability & Statistics for Engineers & Scientists, 9th Edition

Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
Contents......Page 8
Preface......Page 16
Acknowledgments......Page 21
1.1 Overview: Statistical Inference, Samples, Populations, and the Role of Probability......Page 22
1.2 Sampling Procedures; Collection of Data......Page 28
1.3 Measures of Location: The Sample Mean and Median......Page 32
Exercises......Page 34
1.4 Measures of Variability......Page 35
1.5 Discrete and Continuous Data......Page 38
1.6 Statistical Modeling, Scientific Inspection, and Graphical Diagnostics......Page 39
1.7 General Types of Statistical Studies: Designed Experiment, Observational Study, and Retrospective Study......Page 48
Exercises......Page 51
2.1 Sample Space......Page 56
2.2 Events......Page 59
Exercises......Page 63
2.3 Counting Sample Points......Page 65
Exercises......Page 72
2.4 Probability of an Event......Page 73
2.5 Additive Rules......Page 77
Exercises......Page 80
2.6 Conditional Probability, Independence, and the Product Rule......Page 83
Exercises......Page 90
2.7 Bayes’ Rule......Page 93
Exercises......Page 97
Review Exercises......Page 98
2.8 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters......Page 100
3.1 Concept of a Random Variable......Page 102
3.2 Discrete Probability Distributions......Page 105
3.3 Continuous Probability Distributions......Page 108
Exercises......Page 112
3.4 Joint Probability Distributions......Page 115
Exercises......Page 125
Review Exercises......Page 128
3.5 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters......Page 130
4.1 Mean of a Random Variable......Page 132
Exercises......Page 138
4.2 Variance and Covariance of Random Variables......Page 140
Exercises......Page 148
4.3 Means and Variances of Linear Combinations of Random Variables......Page 149
4.4 Chebyshev’s Theorem......Page 156
Exercises......Page 158
Review Exercises......Page 160
4.5 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters......Page 163
5.2 Binomial and Multinomial Distributions......Page 164
Exercises......Page 171
5.3 Hypergeometric Distribution......Page 173
Exercises......Page 178
5.4 Negative Binomial and Geometric Distributions......Page 179
5.5 Poisson Distribution and the Poisson Process......Page 182
Exercises......Page 185
Review Exercises......Page 187
5.6 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters......Page 190
6.1 Continuous Uniform Distribution......Page 192
6.2 Normal Distribution......Page 193
6.3 Areas under the Normal Curve......Page 197
6.4 Applications of the Normal Distribution......Page 203
Exercises......Page 206
6.5 Normal Approximation to the Binomial......Page 208
Exercises......Page 214
6.6 Gamma and Exponential Distributions......Page 215
6.7 Chi-Squared Distribution......Page 221
6.9 Lognormal Distribution......Page 222
6.10 Weibull Distribution (Optional)......Page 224
Exercises......Page 227
Review Exercises......Page 228
6.11 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters......Page 230
7.2 Transformations of Variables......Page 232
7.3 Moments and Moment-Generating Functions......Page 239
Exercises......Page 243
8.1 Random Sampling......Page 246
8.2 Some Important Statistics......Page 248
Exercises......Page 251
8.3 Sampling Distributions......Page 253
8.4 Sampling Distribution of Means and the Central Limit Theorem......Page 254
Exercises......Page 262
8.5 Sampling Distribution of S²......Page 264
8.6 t-Distribution......Page 267
8.7 F-Distribution......Page 272
8.8 Quantile and Probability Plots......Page 275
Exercises......Page 280
Review Exercises......Page 281
8.9 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters......Page 283
9.2 Statistical Inference......Page 286
9.3 Classical Methods of Estimation......Page 287
9.4 Single Sample: Estimating the Mean......Page 290
9.5 Standard Error of a Point Estimate......Page 297
9.6 Prediction Intervals......Page 298
9.7 Tolerance Limits......Page 301
Exercises......Page 303
9.8 Two Samples: Estimating the Difference between Two Means......Page 306
9.9 Paired Observations......Page 312
Exercises......Page 315
9.10 Single Sample: Estimating a Proportion......Page 317
9.11 Two Samples: Estimating the Difference between Two Proportions......Page 321
Exercises......Page 323
9.12 Single Sample: Estimating the Variance......Page 324
9.13 Two Samples: Estimating the Ratio of Two Variances......Page 326
9.14 Maximum Likelihood Estimation (Optional)......Page 328
Exercises......Page 333
Review Exercises......Page 334
9.15 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters......Page 337
10.1 Statistical Hypotheses: General Concepts......Page 340
10.2 Testing a Statistical Hypothesis......Page 342
10.3 The Use of P-Values for Decision Making in Testing Hypotheses......Page 352
Exercises......Page 355
10.4 Single Sample: Tests Concerning a Single Mean......Page 357
10.5 Two Samples: Tests on Two Means......Page 363
10.6 Choice of Sample Size for Testing Means......Page 370
10.7 Graphical Methods for Comparing Means......Page 375
Exercises......Page 377
10.8 One Sample: Test on a Single Proportion......Page 381
10.9 Two Samples: Tests on Two Proportions......Page 384
Exercises......Page 386
10.10 One- and Two-Sample Tests Concerning Variances......Page 387
Exercises......Page 390
10.11 Goodness-of-Fit Test......Page 391
10.12 Test for Independence (Categorical Data)......Page 394
10.13 Test for Homogeneity......Page 397
10.14 Two-Sample Case Study......Page 400
Exercises......Page 403
Review Exercises......Page 405
10.15 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters......Page 407
11.1 Introduction to Linear Regression......Page 410
11.2 The Simple Linear Regression Model......Page 411
11.3 Least Squares and the Fitted Model......Page 415
Exercises......Page 419
11.4 Properties of the Least Squares Estimators......Page 421
11.5 Inferences Concerning the Regression Coefficients......Page 424
11.6 Prediction......Page 429
Exercises......Page 432
11.8 Analysis-of-Variance Approach......Page 435
11.9 Test for Linearity of Regression: Data with Repeated Observations......Page 437
Exercises......Page 442
11.10 Data Plots and Transformations......Page 445
11.11 Simple Linear Regression Case Study......Page 449
11.12 Correlation......Page 451
Exercises......Page 456
Review Exercises......Page 457
11.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters......Page 463
12.1 Introduction......Page 464
12.2 Estimating the Coefficients......Page 465
12.3 Linear Regression Model Using Matrices......Page 468
Exercises......Page 471
12.4 Properties of the Least Squares Estimators......Page 474
12.5 Inferences in Multiple Linear Regression......Page 476
Exercises......Page 482
12.6 Choice of a Fitted Model through Hypothesis Testing......Page 483
12.7 Special Case of Orthogonality (Optional)......Page 488
Exercises......Page 492
12.8 Categorical or Indicator Variables......Page 493
12.9 Sequential Methods for Model Selection......Page 497
12.10 Study of Residuals and Violation of Assumptions (Model Checking)......Page 503
12.11 Cross Validation, Cp, and Other Criteria for Model Selection
......Page 508
Exercises......Page 515
12.12 Special Nonlinear Models for Nonideal Conditions......Page 517
Exercises......Page 521
Review Exercises......Page 522
12.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters......Page 527
13.1 Analysis-of-Variance Technique......Page 528
13.2 The Strategy of Experimental Design......Page 529
13.3 One-Way Analysis of Variance: Completely Randomized Design (One-Way ANOVA)......Page 530
13.4 Tests for the Equality of Several Variances......Page 537
Exercises......Page 539
13.5 Single-Degree-of-Freedom Comparisons......Page 541
13.6 Multiple Comparisons......Page 544
Exercises......Page 550
13.7 Comparing a Set of Treatments in Blocks......Page 553
13.8 Randomized Complete Block Designs......Page 554
13.9 Graphical Methods and Model Checking......Page 561
13.10 Data Transformations in Analysis of Variance......Page 564
Exercises......Page 566
13.11 Random Effects Models......Page 568
13.12 Case Study......Page 572
Exercises......Page 574
Review Exercises......Page 576
13.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters......Page 580
14.1 Introduction......Page 582
14.2 Interaction in the Two-Factor Experiment......Page 583
14.3 Two-Factor Analysis of Variance......Page 586
Exercises......Page 596
14.4 Three-Factor Experiments......Page 600
Exercises......Page 607
14.5 Factorial Experiments for Random Effects and Mixed Models......Page 609
Exercises......Page 613
Review Exercises......Page 615
14.6 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters......Page 617
15.1 Introduction......Page 618
15.2 The 2k Factorial: Calculation of Effects and Analysis of Variance
......Page 619
15.3 Nonreplicated 2k Factorial Experiment
......Page 625
Exercises......Page 630
15.4 Factorial Experiments in a Regression Setting......Page 633
15.5 The Orthogonal Design......Page 638
Exercises......Page 646
15.6 Fractional Factorial Experiments......Page 647
15.7 Analysis of Fractional Factorial Experiments......Page 653
Exercises......Page 655
15.8 Higher Fractions and Screening Designs......Page 657
15.9 Construction of Resolution III and IV Designs with 8, 16, and 32 Design Points......Page 658
15.10 Other Two-Level Resolution III Designs; The Plackett-Burman Designs......Page 659
15.11 Introduction to Response Surface Methodology......Page 660
15.12 Robust Parameter Design......Page 664
Exercises......Page 673
Review Exercises......Page 674
15.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters......Page 675
16.1 Nonparametric Tests......Page 676
16.2 Signed-Rank Test......Page 681
Exercises......Page 684
16.3 Wilcoxon Rank-Sum Test......Page 686
16.4 Kruskal-Wallis Test......Page 689
Exercises......Page 691
16.5 Runs Test......Page 692
16.7 Rank Correlation Coefficient......Page 695
Exercises......Page 698
Review Exercises......Page 700
17.1 Introduction......Page 702
17.3 Purposes of the Control Chart......Page 704
17.4 Control Charts for Variables......Page 705
17.5 Control Charts for Attributes......Page 718
17.6 Cusum Control Charts......Page 726
Review Exercises......Page 727
18.1 Bayesian Concepts......Page 730
18.2 Bayesian Inferences......Page 731
18.3 Bayes Estimates Using Decision Theory Framework......Page 738
Exercises......Page 739
Bibliography......Page 742
Appendix A: Statistical Tables and Proofs......Page 746
Appendix B: Answers to Odd-Numbered Non-Review Exercises......Page 790
C......Page 806
E......Page 807
L......Page 808
N......Page 809
Q......Page 810
T......Page 811
X......Page 812