Probability Concepts in Engineering* Emphasis on Applications in Civil & Environmental EngineeringPDF电子书下载

CHAPTER 1 Roles of Probability and Statistics in Engineering 1

1.1 Introduction 1

1.2 Uncertainty in Engineering 2

1.2.1 Uncertainty Associated with Randomness-The Aleatory Uncertainty 2

1.2.2 Uncertainty Associated with Imperfect Knowledge--The Epistemic Uncertainty 17

1.3 Design and Decision Making under Uncertainty 19

1.3.1 Planning and Design of Transportation Infrastructures 20

1.3.2 Design of Structures and Machines 20

1.3.3 Planning and Design of Hydrosystems 22

1.3.4 Design of Geotechnical Systems 23

1.3.5 Construction Planning and Management 23

1.3.6 Photogrammetric, Geodetic, and Surveying Measurements 24

1.3.7 Applications in Quality Control and Assurance 24

1.4 Concluding Summary 25

References 25

CHAPTER 2 Fundamentals of Probability Models 27

2.1 Events and Probability 27

2.1.1 Characteristics of Problems Involving Probabilities 27

2.1.2 Estimating Probabilities 30

2.2 Elements of Set Theory-Tools for Defining Events 31

2.2.1 Important Definitions 31

2.2.2 Mathematical Operations of Sets 39

2.3 Mathematics of Probability 44

2.3.1 The Addition Rule 45

2.3.2 Conditional Probability 49

2.3.3 The Multiplication Rule 52

2.3.4 The Theorem of Total Probability 57

2.3.5 The Bayes' Theorem 63

2.4 Concluding Summary 65

Problems 66

References 80

CHAPTER 3 Analytical Models of Random Phenomena 81

3.1 Random Variables and Probability Distribution 81

3.1.1 Random Events and Random Variables 81

3.1.2 Probability Distribution of a Random Variable 82

3.1.3 Main Descriptors of a Random Variable 88

3.2 Useful Probability Distributions 96

3.2.1 The Gaussian (or Normal) Distribution 96

3.2.2 The Lognormal Distribution 100

3.2.3 The Bernoulli Sequence and the Binomial Distribution 105

3.2.4 The Geometric Distribution 108

3.2.5 The Negative Binomial Distribution 111

3.2.6 The Poisson Process and the Poisson Distribution 112

3.2.7 The Exponential Distribution 118

3.2.8 The Gamma Distribution 122

3.2.9 The Hypergeometric Distribution 126

3.2.10 The Beta Distribution 127

3.2.11 Other Useful Distributions 131

3.3 Multiple Random Variables 132

3.3.1 Joint and Conditional Probability Distributions 132

3.3.2 Covariance and Correlation 138

3.4 Concluding Summary 141

Problems 141

References 150

CHAPTER 4 Functions of Random Variables 151

4.1 Introduction 151

4.2 Derived Probability Distributions 151

4.2.1 Function of a Single Random Variable 151

4.2.2 Function of Multiple Random Variables 157

4.2.3 Extreme Value Distributions 172

4.3 Moments of Functions of Random Variables 180

4.3.1 Mathematical Expectations of a Function 180

4.3.2 Mean and Variance of a General Function 183

4.4 Concluding Summary 190

Problems 190

References 198

CHAPTER 5 Computer-Based Numerical and Simulation Methods in Probability 199

5.1 Introduction 199

5.2 Numerical and Simulations Methods 200

5.2.1 Essentials of Monte Carlo Simulation 200

5.2.2 Numerical Examples 201

5.2.3 Problems Involving Aleatory and Epistemic Uncertainties 223

5.2.4 MCS Involving Correlated Random Variables 231

5.3 Concluding Summary 242

Problems 242

References and Softwares 244

CHAPTER 6 Statistical Inferences from Observational Data 245

6.1 Role of Statistical Inference in Engineering 245

6.2 Statistical Estimation of Parameters 246

6.2.1 Random Sampling and Point Estimation 246

6.2.2 Sampling Distributions 255

6.3 Testing of Hypotheses 258

6.3.1 Introduction 258

6.3.2 Hypothesis Test Procedure 259

6.4 Confidence Intervals 262

6.4.1 Confidence Interval of the Mean 262

6.4.2 Confidence Interval of the Proportion 268

6.4.3 Confidence Interval of the Variance 269

6.5 Measurement Theory 270

6.6 Concluding Summary 273

Problems 274

References 277

CHAPTER 7 Determination of Probability Distribution Models 278

7.1 Introduction 278

7.2 Probability Papers 279

7.2.1 Utility and Plotting Position 279

7.2.2 The Normal Probability Paper 280

7.2.3 The Lognormal Probability Paper 281

7.2.4 Construction of General Probability Papers 284

7.3 Testing Goodness-of-Fit of Distribution Models 289

7.3.1 The Chi-Square Test for Goodness-of-Fit 289

7.3.2 The Kolmogorov-Smirnov (K-S) Test for Goodness-of-Fit 293

7.3.3 The Anderson-Darling Test for Goodness-of-Fit 296

7.4 Invariance in the Asymptotic Forms of Extremal Distributions 300

7.5 Concluding Summary 301

Problems 302

References 305

CHAPTER 8 Regression and Correlation Analyses 306

8.1 Introduction 306

8.2 Fundamentals of Linear Regression Analysis 306

8.2.1 Regression with Constant Variance 306

8.2.2 Variance in Regression Analysis 308

8.2.3 Confidence Intervals in Regression 309

8.3 Correlation Analysis 311

8.3.1 Estimation of the Correlation Coefficient 312

8.3.2 Regression of Normal Variates 313

8.4 Linear Regression with Nonconstant Variance 318

8.5 Multiple Linear Regression 321

8.6 Nonlinear Regression 325

8.7 Applications of Regression Analysis in Engineering 333

8.8 Concluding Summary 339

Problems 339

References 344

CHAPTER 9 The Bayesian Approach 346

9.1 Introduction 346

9.1.1 Estimation of Parameters 346

9.2 Basic Concepts--The Discrete Case 347

9.3 The Continuous Case 352

9.3.1 General Formulation 352

9.3.2 A Special Application of the Bayesian Updating Process 357

9.4 Bayesian Concept in Sampling Theory 360

9.4.1 General Formulation 360

9.4.2 Sampling from Normal Populations 360

9.4.3 Error in Estimation 362

9.4.4 The Utility of Conjugate Distributions 365

9.5 Estimation of Two Parameters 368

9.6 Bayesian Regression and Correlation Analyses 372

9.6.1 Linear Regression 372

9.6.2 Updating the Regression Parameters 374

9.6.3 Correlation Analysis 375

9.7 Concluding Summary 377

Problems 377

References 381

APPENDICES 383

Appendix A: Probability Tables 383

Table A.1 Standard Normal Probabilities 383

Table A.2 CDF of the Binomial Distribution 387

Table A.3 Critical Values of t-Distribution at Confidence Level (1 -α) = p 392

Table A.4 Critical Values of the x2 Distribution at probability Level α 393

Table A.5 Critical Values of Dan at Significance Level a in the K-S Test 395

Table A.6 Critical Values of the Anderson-Darling Goodness-of-Fit Test 395

Appendix B: Combinatorial Formulas 397

B.1: The Basic Relation 397

B.3: The Binomial Coefficient 398

B.4: The Multinomial Coefficient 399

B.5: Stirling's Formula 399

Appendix C: Derivation of the Poisson Distribution 400

Index 403