Miller & Freund’s Probability and Statistics for Engineers

Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Contents......Page 4
Preface......Page 8
 1.1 Why Study Statistics?......Page 12
 1.3 Statistics and Engineering......Page 13
 1.5 A Case Study: Visually Inspecting Data to Improve Product Quality......Page 14
 1.6 Two Basic Concepts—Population and Sample......Page 16
 Review Exercises......Page 21
 Key Terms......Page 22
 2.1 Pareto Diagrams and Dot Diagrams......Page 23
 2.2 Frequency Distributions......Page 25
 2.3 Graphs of Frequency Distributions......Page 28
 2.4 Stem-and-Leaf Displays......Page 32
 2.5 Descriptive Measures......Page 35
 2.6 Quartiles and Percentiles......Page 40
 2.7 The Calculation of x and s......Page 45
 2.8 A Case Study: Problems with Aggregating Data......Page 50
 Review Exercises......Page 53
 Key Terms......Page 55
 3.1 Sample Spaces and Events......Page 57
 3.2 Counting......Page 61
 3.3 Probability......Page 68
 3.4 The Axioms of Probability......Page 70
 3.5 Some Elementary Theorems......Page 73
 3.6 Conditional Probability......Page 79
 3.7 Bayes’ Theorem......Page 85
 Review Exercises......Page 92
 Key Terms......Page 94
 4.1 Random Variables......Page 95
 4.2 The Binomial Distribution......Page 99
 4.3 The Hypergeometric Distribution......Page 104
 4.4 The Mean and the Variance of a Probability Distribution......Page 108
 4.5 Chebyshev’s Theorem......Page 115
 4.6 The Poisson Distribution and Rare Events......Page 119
 4.7 Poisson Processes......Page 123
 4.8 The Geometric and Negative Binomial Distribution......Page 125
 4.9 The Multinomial Distribution......Page 128
 4.10 Simulation......Page 129
 Review Exercises......Page 133
 Key Terms......Page 134
 5.1 Continuous Random Variables......Page 135
 5.2 The Normal Distribution......Page 141
 5.3 The Normal Approximation to the Binomial Distribution......Page 149
 5.5 The Uniform Distribution......Page 152
 5.6 The Log-Normal Distribution......Page 153
 5.7 The Gamma Distribution......Page 156
 5.8 The Beta Distribution......Page 158
 5.9 TheWeibull Distribution......Page 159
 5.10 Joint Distributions—Discrete and Continuous......Page 162
 5.11 Moment Generating Functions......Page 175
 5.12 Checking If the Data Are Normal......Page 181
 5.13 Transforming Observations to Near Normality......Page 183
 5.14 Simulation......Page 185
 Review Exercises......Page 189
 Key Terms......Page 191
 6.1 Populations and Samples......Page 194
 6.2 The Sampling Distribution of the Mean (σ known)......Page 198
 6.3 The Sampling Distribution of the Mean (σ unknown)......Page 206
 6.4 The Sampling Distribution of the Variance......Page 208
 6.5 Representations of the Normal Theory Distributions......Page 211
 6.6 The Moment Generating Function Method to Obtain Distributions......Page 214
 6.7 Transformation Methods to Obtain Distributions......Page 216
 Review Exercises......Page 222
 Key Terms......Page 223
 7.1 Statistical Approaches to Making Generalizations......Page 224
 7.2 Point Estimation......Page 225
 7.3 Interval Estimation......Page 230
 7.4 Maximum Likelihood Estimation......Page 237
 7.5 Tests of Hypotheses......Page 243
 7.6 Null Hypotheses and Tests of Hypotheses......Page 245
 7.7 Hypotheses Concerning One Mean......Page 250
 7.8 The Relation between Tests and Confidence Intervals......Page 257
 7.9 Power, Sample Size, and Operating Characteristic Curves......Page 258
 Review Exercises......Page 264
 Key Terms......Page 266
 8.1 Experimental Designs for Comparing Two Treatments......Page 267
 8.2 Comparisons—Two Independent Large Samples......Page 268
 8.3 Comparisons—Two Independent Small Samples......Page 273
 8.4 Matched Pairs Comparisons......Page 281
 8.5 Design Issues—Randomization and Pairing......Page 286
 Review Exercises......Page 288
 Key Terms......Page 289
 9.1 The Estimation of Variances......Page 291
 9.2 Hypotheses Concerning One Variance......Page 294
 9.3 Hypotheses Concerning Two Variances......Page 296
 Review Exercises......Page 300
 Key Terms......Page 301
 10.1 Estimation of Proportions......Page 302
 10.2 Hypotheses Concerning One Proportion......Page 309
 10.3 Hypotheses Concerning Several Proportions......Page 311
 10.4 Analysis of r x c Tables......Page 319
 10.5 Goodness of Fit......Page 323
 Review Exercises......Page 326
 Key Terms......Page 327
 11.1 The Method of Least Squares......Page 328
 11.2 Inferences Based on the Least Squares Estimators......Page 337
 11.3 Curvilinear Regression......Page 351
 11.4 Multiple Regression......Page 357
 11.5 Checking the Adequacy of the Model......Page 362
 11.6 Correlation......Page 367
 11.7 Multiple Linear Regression (Matrix Notation)......Page 378
 Review Exercises......Page 383
 Key Terms......Page 386
 12.1 Some General Principles......Page 387
 12.2 Completely Randomized Designs......Page 390
 12.3 Randomized-Block Designs......Page 403
 12.4 Multiple Comparisons......Page 411
 12.5 Analysis of Covariance......Page 416
 Review Exercises......Page 423
 Key Terms......Page 425
 13.1 Two-Factor Experiments......Page 426
 13.2 Multifactor Experiments......Page 433
 13.3 The Graphic Presentation of 22 and 23 Experiments......Page 442
 13.4 Response Surface Analysis......Page 457
 Review Exercises......Page 460
 Key Terms......Page 464
 14.2 The Sign Test......Page 465
 14.3 Rank-Sum Tests......Page 467
 14.4 Correlation Based on Ranks......Page 470
 14.5 Tests of Randomness......Page 473
 14.6 The Kolmogorov-Smirnov and Anderson-Darling Tests......Page 476
 Review Exercises......Page 479
 Key Terms......Page 480
 15.1 Quality-Improvement Programs......Page 481
 15.2 Starting a Quality-Improvement Program......Page 483
 15.3 Experimental Designs for Quality......Page 485
 15.4 Quality Control......Page 487
 15.5 Control Charts for Measurements......Page 489
 15.6 Control Charts for Attributes......Page 494
 15.7 Tolerance Limits......Page 500
 Review Exercises......Page 502
 Key Terms......Page 504
 16.1 Reliability......Page 505
 16.2 Failure-Time Distribution......Page 507
 16.3 The Exponential Model in Life Testing......Page 511
 16.4 The Weibull Model in Life Testing......Page 514
 Review Exercises......Page 519
 Key Terms......Page 520
Appendix A Bibliography......Page 522
Appendix B Statistical Tables......Page 523
 Entering Data......Page 530
 Descriptive Statistics......Page 531
 Sampling Distributions......Page 532
 Regression......Page 533
 One-Way Analysis of Variance (ANOVA)......Page 534
Appendix D Answers to Odd-Numbered Exercises......Page 535
 D......Page 542
 H......Page 543
 M......Page 544
 R......Page 545
 S......Page 546
 Z......Page 547