Probability Concepts in Engineering* Emphasis on Applications in Civil & Environmental Engineering【2025|PDF下载-Epub版本|mobi电子书|kindle百度云盘下载】

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CHAPTER 1 Roles of Probability and Statistics in Engineering1

1.1 Introduction1

1.2 Uncertainty in Engineering2

1.2.1 Uncertainty Associated with Randomness-The Aleatory Uncertainty2

1.2.2 Uncertainty Associated with Imperfect Knowledge--The Epistemic Uncertainty17

1.3 Design and Decision Making under Uncertainty19

1.3.1 Planning and Design of Transportation Infrastructures20

1.3.2 Design of Structures and Machines20

1.3.3 Planning and Design of Hydrosystems22

1.3.4 Design of Geotechnical Systems23

1.3.5 Construction Planning and Management23

1.3.6 Photogrammetric, Geodetic, and Surveying Measurements24

1.3.7 Applications in Quality Control and Assurance24

1.4 Concluding Summary25

References25

CHAPTER 2 Fundamentals of Probability Models27

2.1 Events and Probability27

2.1.1 Characteristics of Problems Involving Probabilities27

2.1.2 Estimating Probabilities30

2.2 Elements of Set Theory-Tools for Defining Events31

2.2.1 Important Definitions31

2.2.2 Mathematical Operations of Sets39

2.3 Mathematics of Probability44

2.3.1 The Addition Rule45

2.3.2 Conditional Probability49

2.3.3 The Multiplication Rule52

2.3.4 The Theorem of Total Probability57

2.3.5 The Bayes' Theorem63

2.4 Concluding Summary65

Problems66

References80

CHAPTER 3 Analytical Models of Random Phenomena81

3.1 Random Variables and Probability Distribution81

3.1.1 Random Events and Random Variables81

3.1.2 Probability Distribution of a Random Variable82

3.1.3 Main Descriptors of a Random Variable88

3.2 Useful Probability Distributions96

3.2.1 The Gaussian (or Normal) Distribution96

3.2.2 The Lognormal Distribution100

3.2.3 The Bernoulli Sequence and the Binomial Distribution105

3.2.4 The Geometric Distribution108

3.2.5 The Negative Binomial Distribution111

3.2.6 The Poisson Process and the Poisson Distribution112

3.2.7 The Exponential Distribution118

3.2.8 The Gamma Distribution122

3.2.9 The Hypergeometric Distribution126

3.2.10 The Beta Distribution127

3.2.11 Other Useful Distributions131

3.3 Multiple Random Variables132

3.3.1 Joint and Conditional Probability Distributions132

3.3.2 Covariance and Correlation138

3.4 Concluding Summary141

Problems141

References150

CHAPTER 4 Functions of Random Variables151

4.1 Introduction151

4.2 Derived Probability Distributions151

4.2.1 Function of a Single Random Variable151

4.2.2 Function of Multiple Random Variables157

4.2.3 Extreme Value Distributions172

4.3 Moments of Functions of Random Variables180

4.3.1 Mathematical Expectations of a Function180

4.3.2 Mean and Variance of a General Function183

4.4 Concluding Summary190

Problems190

References198

CHAPTER 5 Computer-Based Numerical and Simulation Methods in Probability199

5.1 Introduction199

5.2 Numerical and Simulations Methods200

5.2.1 Essentials of Monte Carlo Simulation200

5.2.2 Numerical Examples201

5.2.3 Problems Involving Aleatory and Epistemic Uncertainties223

5.2.4 MCS Involving Correlated Random Variables231

5.3 Concluding Summary242

Problems242

References and Softwares244

CHAPTER 6 Statistical Inferences from Observational Data245

6.1 Role of Statistical Inference in Engineering245

6.2 Statistical Estimation of Parameters246

6.2.1 Random Sampling and Point Estimation246

6.2.2 Sampling Distributions255

6.3 Testing of Hypotheses258

6.3.1 Introduction258

6.3.2 Hypothesis Test Procedure259

6.4 Confidence Intervals262

6.4.1 Confidence Interval of the Mean262

6.4.2 Confidence Interval of the Proportion268

6.4.3 Confidence Interval of the Variance269

6.5 Measurement Theory270

6.6 Concluding Summary273

Problems274

References277

CHAPTER 7 Determination of Probability Distribution Models278

7.1 Introduction278

7.2 Probability Papers279

7.2.1 Utility and Plotting Position279

7.2.2 The Normal Probability Paper280

7.2.3 The Lognormal Probability Paper281

7.2.4 Construction of General Probability Papers284

7.3 Testing Goodness-of-Fit of Distribution Models289

7.3.1 The Chi-Square Test for Goodness-of-Fit289

7.3.2 The Kolmogorov-Smirnov (K-S) Test for Goodness-of-Fit293

7.3.3 The Anderson-Darling Test for Goodness-of-Fit296

7.4 Invariance in the Asymptotic Forms of Extremal Distributions300

7.5 Concluding Summary301

Problems302

References305

CHAPTER 8 Regression and Correlation Analyses306

8.1 Introduction306

8.2 Fundamentals of Linear Regression Analysis306

8.2.1 Regression with Constant Variance306

8.2.2 Variance in Regression Analysis308

8.2.3 Confidence Intervals in Regression309

8.3 Correlation Analysis311

8.3.1 Estimation of the Correlation Coefficient312

8.3.2 Regression of Normal Variates313

8.4 Linear Regression with Nonconstant Variance318

8.5 Multiple Linear Regression321

8.6 Nonlinear Regression325

8.7 Applications of Regression Analysis in Engineering333

8.8 Concluding Summary339

Problems339

References344

CHAPTER 9 The Bayesian Approach346

9.1 Introduction346

9.1.1 Estimation of Parameters346

9.2 Basic Concepts--The Discrete Case347

9.3 The Continuous Case352

9.3.1 General Formulation352

9.3.2 A Special Application of the Bayesian Updating Process357

9.4 Bayesian Concept in Sampling Theory360

9.4.1 General Formulation360

9.4.2 Sampling from Normal Populations360

9.4.3 Error in Estimation362

9.4.4 The Utility of Conjugate Distributions365

9.5 Estimation of Two Parameters368

9.6 Bayesian Regression and Correlation Analyses372

9.6.1 Linear Regression372

9.6.2 Updating the Regression Parameters374

9.6.3 Correlation Analysis375

9.7 Concluding Summary377

Problems377

References381

APPENDICES383

Appendix A: Probability Tables383

Table A.1 Standard Normal Probabilities383

Table A.2 CDF of the Binomial Distribution387

Table A.3 Critical Values of t-Distribution at Confidence Level (1 -α) = p392

Table A.4 Critical Values of the x2 Distribution at probability Level α393

Table A.5 Critical Values of Dan at Significance Level a in the K-S Test395

Table A.6 Critical Values of the Anderson-Darling Goodness-of-Fit Test395

Appendix B: Combinatorial Formulas397

B.1: The Basic Relation397

B.3: The Binomial Coefficient398

B.4: The Multinomial Coefficient399

B.5: Stirling's Formula399

Appendix C: Derivation of the Poisson Distribution400

Index403