Cover image for Introduction to probability and statistics for engineers and scientists
Title:
Introduction to probability and statistics for engineers and scientists
Author:
Ross, Sheldon M. (Sheldon Mark)
Edition:
Second edition.
Publication Information:
San Diego, Calif. : Harcourt/Academic, [2000]

©2000
Physical Description:
xiv, 578 pages : illustrations ; 25 cm
General Note:
Previous ed.: New York : Chichester : Wiley, c1987.
Language:
English
ISBN:
9780125984720
Format :
Book

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Central Library TA340 .R67 2000 Adult Non-Fiction Central Closed Stacks
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Summary

Summary

Suited for a first course in applied probability and statistics for engineering or science majors, this is a superior textbook. Introduction to Probability and Statistics for Engineers and Scientists, Second Edition, includes expanded coverage of quality control, and offers unique software that automates the computations required for exercises, as well as illustrating the main concepts of probability. The author emphasizes the manner in which probability yields insight into statistical problems; ultimately resulting in an intuitive understanding of the statistical procedures most often used by practicing engineers and scientists. Real data sets are incorporated in a wide variety of exercises and examples throughout the book, and this emphasis on data motivates the probability coverage.


Author Notes

Sheldon M. Ross has published numerous textbooks and technical articles in the areas of statistics and applied probability. Professor Ross is the founding and continuing editor of the journal Probability in the Engineering and Informational Sciences, published by Cambridge University Press. He is a fellow of the Institute of Mathematical Statistics and a recipient of the Humboldt U.S. Senior Scientist award.


Table of Contents

Prefacep. xiii
Chapter 1 Introduction to Statisticsp. 1
1.1 Introductionp. 1
1.2 Data Collection and Descriptive Statisticsp. 1
1.3 Inferential Statistics and Probability Modelsp. 2
1.4 Populations and Samplesp. 3
1.5 A Brief History of Statisticsp. 3
Problemsp. 7
Chapter 2 Descriptive Statisticsp. 9
2.1 Introductionp. 9
2.2 Describing Data Setsp. 9
2.2.1 Frequency Tables and Graphsp. 10
2.2.2 Relative Frequency Tables and Graphsp. 10
2.2.3 Grouped Data, Histograms, Ogives, and Stem and Leaf Plotsp. 14
2.3 Summarizing Data Setsp. 19
2.3.1 Sample Mean, Sample Median, and Sample Modep. 19
2.3.2 Sample Variance and Sample Standard Deviationp. 23
2.3.3 Sample Percentiles and Box Plotsp. 25
2.4 Chebyshev's Inequalityp. 29
2.5 Normal Data Setsp. 30
2.6 Paired Data Sets and the Sample Correlation Coefficientp. 34
Problemsp. 40
Chapter 3 Elements of Probabilityp. 59
3.1 Introductionp. 59
3.2 Sample Space and Eventsp. 60
3.3 Venn Diagrams and the Algebra of Eventsp. 62
3.4 Axioms of Probabilityp. 63
3.5 Sample Spaces Having Equally Likely Outcomesp. 65
3.6 Conditional Probabilityp. 70
3.7 Bayes' Formulap. 74
3.8 Independent Eventsp. 79
Problemsp. 82
Chapter 4 Random Variables and Expectationp. 89
4.1 Random Variablesp. 89
4.2 Types of Random Variablesp. 91
4.3 Jointly Distributed Random Variablesp. 95
4.3.1 Independent Random Variablesp. 100
4.3.2 Conditional Distributionsp. 103
4.4 Expectationp. 105
4.5 Properties of the Expected Valuep. 110
4.5.1 Expected Value of Sums of Random Variablesp. 113
4.6 Variancep. 116
4.7 Covariance and Variance of Sums of Random Variablesp. 119
4.8 Moment Generating Functionsp. 123
4.9 Chebyshev's Inequality and the Weak Law of Large Numbersp. 124
Problemsp. 127
Chapter 5 Special Random Variablesp. 137
5.1 The Bernoulli and Binomial Random Variablesp. 137
5.1.1 Computing the Binomial Distribution Functionp. 142
5.2 The Poisson Random Variablep. 144
5.2.1 Computing the Poisson Distribution Functionp. 150
5.3 The Hypergeometric Random Variablep. 150
5.4 The Uniform Random Variablep. 154
5.5 Normal Random Variablesp. 160
5.6 Exponential Random Variablesp. 167
5.6.1 The Poisson Processp. 171
5.7 The Gamma Distributionp. 173
5.8 Distributions Arising from the Normalp. 177
5.8.1 The Chi-Square Distributionp. 177
5.8.1.1 The Relation between Chi-Square and Gamma Random Variablesp. 178
5.8.2 The t-Distributionp. 180
5.8.3 The F-Distributionp. 182
Problemsp. 184
Chapter 6 Distributions of Sampling Statisticsp. 191
6.1 Introductionp. 191
6.2 The Sample Meanp. 192
6.3 The Central Limit Theoremp. 193
6.3.1 Approximate Distribution of the Sample Meanp. 200
6.3.2 How Large a Sample Is Neededp. 203
6.4 The Sample Variancep. 203
6.5 Sampling Distributions from a Normal Populationp. 204
6.5.1 Distribution of the Sample Meanp. 204
6.5.2 Joint Distribution of X and S[superscript 2]p. 204
6.6 Sampling from A Finite Populationp. 206
Problemsp. 210
Chapter 7 Parameter Estimationp. 217
7.1 Introductionp. 217
7.2 Maximum Likelihood Estimatorsp. 218
7.3 Interval Estimatesp. 223
7.3.1 Confidence Interval for a Normal Mean When the Variance Is Unknownp. 229
7.3.2 Confidence Intervals for the Variance of a Normal Distributionp. 234
7.4 Estimating the Difference in Means of Two Normal Populationsp. 235
7.5 Approximate Confidence Interval for the Mean of a Bernoulli Random Variablep. 242
7.6 Confidence Interval of the Mean of the Exponential Distributionp. 246
7.7 Evaluating a Point Estimatorp. 247
7.8 The Bayes Estimatorp. 253
Problemsp. 258
Chapter 8 Hypothesis Testingp. 271
8.1 Introductionp. 271
8.2 Significance Levelsp. 272
8.3 Tests Concerning the Mean of a Normal Populationp. 273
8.3.1 Case of Known Variancep. 273
8.3.1.1 One-Sided Testsp. 279
8.3.2 Case of Unknown Variance: The t-Testp. 284
8.4 Testing the Equality of Means of Two Normal Populationsp. 291
8.4.1 Case of Known Variancesp. 291
8.4.2 Case of Unknown Variancesp. 293
8.4.3 Case of Unknown and Unequal Variancesp. 297
8.4.4 The Paired t-Testp. 297
8.5 Hypothesis Tests Concerning the Variance of a Normal Populationp. 299
8.5.1 Testing for the Equality of Variances of Two Normal Populationsp. 301
8.6 Hypothesis Tests in Bernoulli Populationsp. 302
8.6.1 Testing the Equality of Parameters in Two Bernoulli Populationsp. 305
8.6.1.1 Computations for the Fisher-Irwin Testp. 306
8.7 Tests Concerning the Mean of a Poisson Distributionp. 307
8.7.1 Testing the Relationship between Two Poisson Parametersp. 308
Problemsp. 309
Chapter 9 Regressionp. 325
9.1 Introductionp. 325
9.2 Least Squares Estimators of the Regression Parametersp. 327
9.3 Distribution of the Estimatorsp. 330
9.4 Statistical Inferences about the Regression Parametersp. 335
9.4.1 Inferences Concerning [beta]p. 335
9.4.1.1 Regression to the Meanp. 339
9.4.2 Inferences Concerning [alpha]p. 343
9.4.3 Inferences Concerning the Mean Response [alpha] + [beta]Xp. 343
9.4.4 Prediction Interval of a Future Responsep. 345
9.4.5 Summary of Distributional Resultsp. 347
9.5 The Coefficient of Determination and the Sample Correlation Coefficientp. 348
9.6 Analysis of Residuals: Assessing the Modelp. 350
9.7 Transforming to Linearityp. 352
9.8 Weighted Least Squaresp. 356
9.9 Polynomial Regressionp. 362
9.10 Multiple Linear Regressionp. 365
9.10.1 Predicting Future Responsesp. 376
Problemsp. 381
Chapter 10 Analysis of Variancep. 405
10.1 Introductionp. 405
10.2 An Overviewp. 406
10.3 One-Way Analysis of Variancep. 408
10.3.1 Multiple Comparisons of Sample Meansp. 414
10.3.2 One-Way Analysis of Variance with Unequal Sample Sizesp. 416
10.4 Two-Factor Analysis of Variance: Introduction and Parameter Estimationp. 417
10.5 Two-Factor Analysis of Variance: Testing Hypothesesp. 421
10.6 Two-Way Analysis of Variance with Interactionp. 425
Problemsp. 434
Chapter 11 Goodness of Fit Tests and Categorical Data Analysisp. 447
11.1 Introductionp. 447
11.2 Goodness of Fit Tests When All Parameters Are Specifiedp. 448
11.2.1 Determining the Critical Region by Simulationp. 453
11.3 Goodness of Fit Tests When Some Parameters Are Unspecifiedp. 456
11.4 Tests of Independence in Contingency Tablesp. 458
11.5 Tests of Independence in Contingency Tables Having Fixed Marginal Totalsp. 463
11.6 The Kolmogorov-Smirnov Goodness of Fit Test for Continuous Datap. 466
Problemsp. 470
Chapter 12 Nonparametric Hypothesis Testsp. 479
12.1 Introductionp. 479
12.2 The Sign Testp. 479
12.3 The Signed Rank Testp. 483
12.4 The Two-Sample Problemp. 488
12.4.1 The Classical Approximation and Simulationp. 492
12.5 The Runs Test for Randomnessp. 494
Problemsp. 499
Chapter 13 Quality Controlp. 507
13.1 Introductionp. 507
13.2 Control Charts for Average Values: The X-Control Chartsp. 508
13.2.1 Case of Unknown [mu] and [sigma]p. 511
13.3 S-Control Chartsp. 515
13.4 Control Charts for the Fraction Defectivep. 518
13.5 Control Charts for Number of Defectsp. 520
13.6 Other Control Charts for Detecting Changes in the Population Meanp. 523
13.6.1 Moving-Average Control Chartsp. 524
13.6.2 Exponentially Weighted Moving-Average Control Chartsp. 526
13.6.3 Cumulative Sum Control Chartsp. 530
Problemsp. 533
Chapter 14 Life Testingp. 541
14.1 Introductionp. 541
14.2 Hazard Rate Functionsp. 541
14.3 The Exponential Distribution in Life Testingp. 544
14.3.1 Simultaneous Testing -- Stopping at the rth Failurep. 544
14.3.2 Sequential Testingp. 549
14.3.3 Simultaneous Testing -- Stopping by a Fixed Timep. 553
14.3.4 The Bayesian Approachp. 555
14.4 A Two-Sample Problemp. 557
14.5 The Weibull Distribution in Life Testingp. 558
14.5.1 Parameter Estimation by Least Squaresp. 560
Problemsp. 562
Appendix of Tablesp. 569
Indexp. 575

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