Introduction to probability and statistics for engineers and scientists

Reviews fundamental concepts and applications of probability and statistics. After a general overview, it considers special types of random variables, using examples which illustrate their wide variety of applications. Also examines their calculation and presents computer programs that calculate the probability distribution, and the inverses of binomial, poisson, normal, t, F, and Chi-square distributions. Coverage includes such topics as the sample mean, sample variance, sample median, as well as histograms, empirical distribution functions, and stem-and-leaf plots. A program for computing sample mean and sample variance for a given data set is included. A diskette of 35 programs for the IBM PC is available, giving exact answers or approximations where appropriate.

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.

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

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