Probability and Statistics for Engineers and Scientists

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