Introduction to probability and statistics for engineers and scientists

Cover Page
......Page 1
Title Page
......Page 4
Copyright Page......Page 5
Dedication
......Page 6
Preface......Page 14
Table of Contents......Page 8
1.2 Data Collection and Descriptive Statistics......Page 18
1.3 Inferential Statistics and Probability Models......Page 19
1.5 A Brief History of Statistics......Page 20
Problems......Page 24
2.2 Describing Data Sets......Page 26
2.2.2 Relative Frequency Tables and Graphs......Page 27
2.2.3 Grouped Data, Histograms, Ogives, and Stem and Leaf Plots......Page 31
2.3.1 Sample Mean, Sample Median, and Sample Mode......Page 34
2.3.2 Sample Variance and Sample Standard Deviation......Page 39
2.3.3 Sample Percentiles and Box Plots......Page 41
2.4 Chebyshev’s Inequality......Page 44
2.5 Normal Data Sets......Page 48
2.6 Paired Data Sets and the Sample Correlation Coefficient......Page 50
Problems......Page 58
3.1 Introduction......Page 72
3.2 Sample Space and Events......Page 73
3.3 Venn Diagrams and the Algebra of Events......Page 75
3.4 Axioms of Probability......Page 76
3.5 Sample Spaces Having Equally Likely Outcomes......Page 78
3.6 Conditional Probability......Page 84
3.7 Bayes’ Formula......Page 87
3.8 Independent Events......Page 93
Problems......Page 97
4.1 Random Variables......Page 106
4.2 Types of Random Variables......Page 109
4.3 Jointly Distributed Random Variables......Page 112
4.3.1 Independent Random Variables......Page 118
*4.3.2 Conditional Distributions......Page 122
4.4 Expectation......Page 124
4.5 Properties of the Expected Value......Page 128
4.5.1 Expected Value of Sums of Random Variables......Page 132
4.6 Variance......Page 135
4.7 Covariance and Variance of Sums of Random Variables......Page 138
4.8 Moment Generating Functions......Page 142
4.9 Chebyshev’s Inequality and the Weak Law of Large Numbers......Page 144
Problems......Page 147
5.1 The Bernoulli and Binomial Random Variables......Page 158
5.1.1 Computing the Binomial Distribution Function......Page 164
5.2 The Poisson Random Variable......Page 165
5.2.1 Computing the Poisson Distribution Function......Page 172
5.3 The Hypergeometric Random Variable......Page 173
5.4 The Uniform Random Variable......Page 177
5.5 Normal Random Variables......Page 185
5.6 Exponential Random Variables......Page 193
*5.6.1 The Poisson Process......Page 197
*5.7 The Gamma Distribution......Page 200
5.8.1 The Chi-Square Distribution......Page 203
5.8.2 The t-Distribution......Page 207
5.8.3 The F-Distribution......Page 209
*5.9 The Logistics Distribution......Page 210
Problems......Page 212
6.1 Introduction......Page 220
6.2 The Sample Mean......Page 221
6.3 The Central Limit Theorem......Page 223
6.3.1 Approximate Distribution of the Sample Mean......Page 229
6.3.2 How Large a Sample Is Needed?......Page 231
6.4 The Sample Variance......Page 232
6.5 Sampling Distributions from a Normal Population......Page 233
6.5.2 Joint Distribution of X and S2......Page 234
6.6 Sampling from a Finite Population......Page 236
Problems......Page 240
7.1 Introduction......Page 248
7.2 Maximum Likelihood Estimators......Page 249
*7.2.1 Estimating Life Distributions......Page 257
7.3 Interval Estimates......Page 259
7.3.1 Confidence Interval for a Normal Mean When the Variance Is Unknown......Page 265
7.3.2 Confidence Intervals for the Variance of a Normal Distribution......Page 270
7.4 Estimating the Difference in Means of Two Normal Populations......Page 272
7.5 Approximate Confidence Interval for the Mean of a Bernoulli Random Variable......Page 279
*7.6 Confidence Interval of the Mean of the Exponential Distribution......Page 284
*7.7 Evaluating a Point Estimator......Page 285
*7.8 The Bayes Estimator......Page 291
Problems......Page 296
8.1 Introduction......Page 310
8.2 Significance Levels......Page 311
8.3.1 Case of Known Variance......Page 312
8.3.2 Case of Unknown Variance: The t-Test......Page 324
8.4.1 Case of Known Variances......Page 331
8.4.2 Case of Unknown Variances......Page 333
8.4.3 Case of Unknown and Unequal Variances......Page 337
8.4.4 The Paired t-Test......Page 338
8.5 Hypothesis Tests Concerning the Variance of a Normal Population......Page 340
8.5.1 Testing for the Equality of Variances of Two Normal Populations......Page 341
8.6 Hypothesis Tests in Bernoulli Populations......Page 342
8.6.1 Testing the Equality of Parameters in Two Bernoulli Populations......Page 346
8.7 Tests Concerning the Mean of a Poisson Distribution......Page 349
8.7.1 Testing the Relationship Between Two Poisson Parameters......Page 350
Problems......Page 353
9.1 Introduction......Page 370
9.2 Least Squares Estimators of the Regression Parameters......Page 372
9.3 Distribution of the Estimators......Page 374
9.4 Statistical Inferences about the Regression Parameters......Page 380
9.4.1 Inferences Concerning β......Page 381
9.4.2 Inferences Concerning α......Page 389
9.4.3 Inferences Concerning the Mean Response α+βx0......Page 390
9.4.4 Prediction Interval of a Future Response......Page 392
9.4.5 Summary of Distributional Results......Page 394
9.5 The Coefficient of Determination and the Sample Correlation Coefficient......Page 395
9.6 Analysis of Residuals: Assessing the Model......Page 397
9.7 Transforming to Linearity......Page 400
9.8 Weighted Least Squares......Page 403
9.9 Polynomial Regression......Page 410
*9.10 Multiple Linear Regression......Page 413
9.10.1 Predicting Future Responses......Page 424
9.11 Logistic Regression Models for Binary Output Data......Page 429
Problems......Page 432
10.1 Introduction......Page 458
10.2 An Overview......Page 459
10.3 One-Way Analysis of Variance......Page 461
10.3.1 Multiple Comparisons of Sample Means......Page 469
10.3.2 One-Way Analysis of Variance with Unequal Sample Sizes......Page 471
10.4 Two-Factor Analysis of Variance:Introduction and Parameter Estimation......Page 473
10.5 Two-Factor Analysis of Variance:Testing Hypotheses......Page 477
10.6 Two-Way Analysis of Variance with Interaction......Page 482
Problems......Page 490
11.1 Introduction......Page 502
11.2 Goodness of Fit Tests When All Parameters are Specified......Page 503
11.2.1 Determining the Critical Region by Simulation......Page 509
11.3 Goodness of Fit Tests When Some Parameters are Unspecified......Page 512
11.4 Tests of Independence in Contingency Tables......Page 514
11.5 Tests of Independence in Contingency Tables Having Fixed Marginal Totals......Page 518
*11.6 The Kolmogorov–Smirnov Goodness of Fit Test for Continuous Data......Page 523
Problems......Page 527
12.2 The Sign Test......Page 534
12.3 The Signed Rank Test......Page 538
12.4 The Two-Sample Problem......Page 544
*12.4.1 The Classical Approximation and Simulation......Page 548
12.5 The Runs Test for Randomness......Page 552
Problems......Page 556
13.1 Introduction......Page 564
13.2 Control Charts for Average Values:The X-Control Chart......Page 565
13.2.1 Case of Unknown μ and σ......Page 568
13.3 S-Control Charts......Page 573
13.4 Control Charts for the Fraction Defective......Page 576
13.5 Control Charts for Number of Defects......Page 578
13.6.1 Moving-Average Control Charts......Page 582
13.6.2 Exponentially Weighted Moving-Average Control Charts......Page 584
13.6.3 Cumulative Sum Control Charts......Page 590
Problems......Page 592
14.2 Hazard Rate Functions......Page 600
14.3.1 Simultaneous Testing — Stopping at the rth Failure......Page 603
14.3.2 Sequential Testing......Page 609
14.3.3 Simultaneous Testing — Stopping by a Fixed Time......Page 613
14.3.4 The Bayesian Approach......Page 615
14.4 A Two-Sample Problem......Page 617
14.5 The Weibull Distribution in Life Testing......Page 619
14.5.1 Parameter Estimation by Least Squares......Page 621
Problems......Page 623
15.1 Introduction......Page 630
15.2 Random Numbers......Page 631
15.2.1 The Monte Carlo Simulation Approach......Page 633
15.3 The Bootstrap Method......Page 634
15.4 Permutation Tests......Page 641
15.4.1 Normal Approximations in Permutation Tests......Page 644
15.4.2 Two-Sample Permutation Tests......Page 648
15.5 Generating Discrete Random Variables......Page 649
15.6 Generating Continuous Random Variables......Page 651
15.6.1 Generating a Normal Random Variable......Page 653
15.7 Determining the Number of Simulation Runs in a Monte Carlo Study......Page 654
Problems......Page 655
Appendix of Tables......Page 658
Index......Page 664