Introduction to Probability and Statistics for Engineers and Scientists, Third Edition

INTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS......Page 4
CONTENTS......Page 8
PREFACE......Page 14
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
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
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
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 143
4.9 CHEBYSHEV’S INEQUALITY AND THE WEAK LAW OF LARGE NUMBERS......Page 144
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 192
*5.6.1 The Poisson Process......Page 196
*5.7 THE GAMMA DISTRIBUTION......Page 199
5.8.1 The Chi-Square Distribution......Page 202
*5.8.1.1 THE RELATION BETWEEN CHI-SQUARE AND GAMMA RANDOM VARIABLES......Page 204
5.8.2 The t-Distribution......Page 206
5.8.3 The F-Distribution......Page 208
*5.9 THE LOGISTICS DISTRIBUTION......Page 209
6.1 INTRODUCTION......Page 218
6.2 THE SAMPLE MEAN......Page 219
6.3 THE CENTRAL LIMIT THEOREM......Page 221
6.3.1 Approximate Distribution of the Sample Mean......Page 227
6.3.2 How Large a Sample Is Needed?......Page 229
6.4 THE SAMPLE VARIANCE......Page 230
6.5 SAMPLING DISTRIBUTIONS FROM A NORMAL POPULATION......Page 231
6.5.2 Joint Distribution of X and S2......Page 232
6.6 SAMPLING FROM A FINITE POPULATION......Page 234
7.1 INTRODUCTION......Page 246
7.2 MAXIMUM LIKELIHOOD ESTIMATORS......Page 247
*7.2.1 Estimating Life Distributions......Page 255
7.3 INTERVAL ESTIMATES......Page 257
7.3.1 Confidence Interval for a Normal Mean When the Variance is Unknown......Page 263
7.3.2 Confidence Intervals for the Variance of a Normal Distribution......Page 268
7.4 ESTIMATING THE DIFFERENCE IN MEANS OF TWO NORMAL POPULATIONS......Page 270
7.5 APPROXIMATE CONFIDENCE INTERVAL FOR THE MEAN OF A BERNOULLI RANDOM VARIABLE......Page 277
*7.6 CONFIDENCE INTERVAL OF THE MEAN OF THE EXPONENTIAL DISTRIBUTION......Page 282
*7.7 EVALUATING A POINT ESTIMATOR......Page 283
*7.8 THE BAYES ESTIMATOR......Page 289
8.1 INTRODUCTION......Page 308
8.2 SIGNIFICANCE LEVELS......Page 309
8.3.1 Case of Known Variance......Page 310
8.3.2 Case of Unknown Variance: The t-Test......Page 322
8.4.1 Case of Known Variances......Page 329
8.4.2 Case of Unknown Variances......Page 331
8.4.3 Case of Unknown and Unequal Variances......Page 335
8.4.4 The Paired t-Test......Page 336
8.5 HYPOTHESIS TESTS CONCERNING THE VARIANCE OF A NORMAL POPULATION......Page 338
8.5.1 Testing for the Equality of Variances of Two Normal Populations......Page 339
8.6 HYPOTHESIS TESTS IN BERNOULLI POPULATIONS......Page 340
8.6.1 Testing the Equality of Parameters in Two Bernoulli Populations......Page 344
8.7 TESTS CONCERNING THE MEAN OF A POISSON DISTRIBUTION......Page 347
8.7.1 Testing the Relationship Between Two Poisson Parameters......Page 348
9.1 INTRODUCTION......Page 368
9.2 LEAST SQUARES ESTIMATORS OF THE REGRESSION PARAMETERS......Page 370
9.3 DISTRIBUTION OF THE ESTIMATORS......Page 372
9.4 STATISTICAL INFERENCES ABOUT THE REGRESSION PARAMETERS......Page 378
9.4.1 Inferences Concerning β......Page 379
9.4.1.1 REGRESSION TO THE MEAN......Page 383
9.4.2 Inferences Concerning α......Page 387
9.4.3 Inferences Concerning the Mean Response α+βx0......Page 388
9.4.4 Prediction Interval of a Future Response......Page 390
9.4.5 Summary of Distributional Results......Page 392
9.5 THE COEFFICIENT OF DETERMINATION AND THE SAMPLE CORRELATION COEFFICIENT......Page 393
9.6 ANALYSIS OF RESIDUALS: ASSESSING THE MODEL......Page 395
9.7 TRANSFORMING TO LINEARITY......Page 398
9.8 WEIGHTED LEAST SQUARES......Page 401
9.9 POLYNOMIAL REGRESSION......Page 408
*9.10 MULTIPLE LINEAR REGRESSION......Page 411
9.10.1 Predicting Future Responses......Page 422
9.11 LOGISTIC REGRESSION MODELS FOR BINARY OUTPUT DATA......Page 427
10.1 INTRODUCTION......Page 456
10.2 AN OVERVIEW......Page 457
10.3 ONE-WAY ANALYSIS OF VARIANCE......Page 459
10.3.1 Multiple Comparisons of Sample Means......Page 467
10.3.2 One-Way Analysis of Variance with Unequal Sample Sizes......Page 469
10.4 TWO-FACTOR ANALYSIS OF VARIANCE: INTRODUCTION AND PARAMETER ESTIMATION......Page 471
10.5 TWO-FACTOR ANALYSIS OF VARIANCE: TESTING HYPOTHESES......Page 475
10.6 TWO-WAY ANALYSIS OF VARIANCE WITH INTERACTION......Page 480
11.1 INTRODUCTION......Page 500
11.2 GOODNESS OF FIT TESTS WHEN ALL PARAMETERS ARE SPECIFIED......Page 501
11.2.1 Determining the Critical Region by Simulation......Page 507
11.3 GOODNESS OF FIT TESTS WHEN SOME PARAMETERS ARE UNSPECIFIED......Page 510
11.4 TESTS OF INDEPENDENCE IN CONTINGENCY TABLES......Page 512
11.5 TESTS OF INDEPENDENCE IN CONTINGENCY TABLES HAVING FIXED MARGINAL TOTALS......Page 516
*11.6 THE KOLMOGOROV–SMIRNOV GOODNESS OF FIT TEST FOR CONTINUOUS DATA......Page 521
12.2 THE SIGN TEST......Page 532
12.3 THE SIGNED RANK TEST......Page 536
12.4 THE TWO-SAMPLE PROBLEM......Page 542
12.4.1 The Classical Approximation and Simulation......Page 546
12.5 THE RUNS TEST FOR RANDOMNESS......Page 550
13.1 INTRODUCTION......Page 562
13.2 CONTROL CHARTS FOR AVERAGE VALUES: THE X -CONTROL CHART......Page 563
13.2.1 Case of Unknown μ and σ......Page 566
13.3 S-CONTROL CHARTS......Page 571
13.4 CONTROL CHARTS FOR THE FRACTION DEFECTIVE......Page 574
13.5 CONTROL CHARTS FOR NUMBER OF DEFECTS......Page 576
13.6.1 Moving-Average Control Charts......Page 580
13.6.2 Exponentially Weighted Moving-Average Control Charts......Page 582
13.6.3 Cumulative Sum Control Charts......Page 588
14.2 HAZARD RATE FUNCTIONS......Page 598
14.3.1 Simultaneous Testing — Stopping at the r th Failure......Page 601
14.3.2 Sequential Testing......Page 607
14.3.3 Simultaneous Testing — Stopping by a Fixed Time......Page 611
14.3.4 The Bayesian Approach......Page 613
14.4 A TWO-SAMPLE PROBLEM......Page 615
14.5 THE WEIBULL DISTRIBUTION IN LIFE TESTING......Page 617
14.5.1 Parameter Estimation by Least Squares......Page 619
APPENDIX OF TABLES......Page 628
INDEX......Page 634