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| Preface | |
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| Roles of Probability and Statistics in Engineering | |
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| Introduction | |
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| Uncertainty in Engineering | |
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| Uncertainty Associated with Randomness-The Aleatory Uncertainty | |
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| Uncertainty Associated with Imperfect Knowledge-The Epistemic Uncertainty | |
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| Design and Decision Making under Uncertainty | |
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| Planning and Design of Transportation Infrastructures | |
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| Design of Structures and Machines | |
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| Planning and Design of Hydrosystems | |
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| Design of Geotechnical Systems | |
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| Construction Planning and Management | |
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| Photogrammetric, Geodetic, and Surveying Measurements | |
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| Applications in Quality Control and Assurance | |
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| Concluding Summary | |
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| References | |
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| Fundamentals of Probability Models | |
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| Events and Probability | |
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| Characteristics of Problems Involving Probabilities | |
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| Estimating Probabilities | |
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| Elements of Set Theory-Tools for Defining Events | |
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| Important Definitions | |
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| Mathematical Operations of Sets | |
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| Mathematics of Probability | |
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| The Addition Rule | |
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| Conditional Probability | |
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| The Multiplication Rule | |
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| The Theorem of Total Probability | |
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| The Bayes' Theorem | |
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| Concluding Summary | |
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| Problems | |
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| References | |
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| Analytical Models of Random Phenomena | |
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| Random Variables and Probability Distribution | |
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| Random Events and Random Variables | |
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| Probability Distribution of a Random Variable | |
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| Main Descriptors of a Random Variable | |
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| Useful Probability Distributions | |
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| The Gaussian (or Normal) Distribution | |
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| The Lognormal Distribution | |
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| The Bernoulli Sequence and the Binomial Distribution | |
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| The Geometric Distribution | |
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| The Negative Binomial Distribution | |
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| The Poisson Process and the Poisson Distribution | |
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| The Exponential Distribution | |
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| The Gamma Distribution | |
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| The Hypergeometric Distribution | |
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| The Beta Distribution | |
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| Other Useful Distributions | |
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| Multiple Random Variables | |
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| Joint and Conditional Probability Distributions | |
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| Covariance and Correlation | |
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| Concluding Summary | |
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| Problems | |
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| References | |
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| Functions of Random Variables | |
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| Introduction | |
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| Derived Probability Distributions | |
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| Function of a Single Random Variable | |
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| Function of Multiple Random Variables | |
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| Extreme Value Distributions | |
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| Moments of Functions of Random Variables | |
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| Mathematical Expectations of a Function | |
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| Mean and Variance of a General Function | |
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| Concluding Summary | |
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| Problems | |
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| References | |
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| Computer-Based Numerical and Simulation Methods in Probability | |
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| Introduction | |
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| Numerical and Simulations Methods | |
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| Essentials of Monte Carlo Simulation | |
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| Numerical Examples | |
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| Problems Involving Aleatory and Epistemic Uncertainties | |
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| MCS Involving Correlated Random Variables | |
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| Concluding Summary | |
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| Problems | |
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| References and Softwares | |
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| Statistical Inferences from Observational Data | |
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| Role of Statistical Inference in Engineering | |
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| Statistical Estimation of Parameters | |
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| Random Sampling and Point Estimation | |
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| Sampling Distributions | |
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| Testing of Hypotheses | |
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| Introduction | |
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| Hypothesis Test Procedure | |
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| Confidence Intervals | |
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| Confidence Interval of the Mean | |
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| Confidence Interval of the Proportion | |
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| Confidence Interval of the Variance | |
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| Measurement Theory | |
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| Concluding Summary | |
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| Problems | |
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| References | |
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| Determination of Probability Distribution Models | |
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| Introduction | |
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| Probability Papers | |
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| Utility and Plotting Position | |
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| The Normal Probability Paper | |
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| The Lognormal Probability Paper | |
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| Construction of General Probability Papers | |
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| Testing Goodness-of-Fit of Distribution Models | |
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| The Chi-Square Test for Goodness-of-Fit | |
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| The Kolmogorov-Smirnov (K-S) Test for Goodness-of-Fit | |
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| The Anderson-Darling Test for Goodness-of-Fit | |
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| Invariance in the Asymptotic Forms of Extremal Distributions | |
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| Concluding Summary | |
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| Problems | |
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| References | |
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| Regression and Correlation Analyses | |
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| Introduction | |
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| Fundamentals of Linear Regression Analysis | |
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| Regression with Constant Variance | |
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| Variance in Regression Analysis | |
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| Confidence Intervals in Regression | |
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| Correlation Analysis | |
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| Estimation of the Correlation Coefficient | |
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| Regression of Normal Variates | |
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| Linear Regression with Nonconstant Variance | |
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| Multiple Linear Regression | |
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| Nonlinear Regression | |
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| Applications of Regression Analysis in Engineering | |
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| Concluding Summary | |
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| Problems | |
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| References | |
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| The Bayesian Approach | |
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| Introduction | |
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| Estimation of Parameters | |
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| Basic Concepts-The Discrete Case | |
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| The Continuous Case | |
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| General Formulation | |
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| A Special Application of the Bayesian Updating Process | |
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| Bayesian Concept in Sampling Theory | |
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| General Formulation | |
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| Sampling from Normal Populations | |
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| Error in Estimation | |
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| The Utility of Conjugate Distributions | |
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| Estimation of Two Parameters | |
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| Bayesian Regression and Correlation Analyses | |
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| Linear Regression | |
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| Updating the Regression Parameters | |
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| Correlation Analysis | |
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| Concluding Summary | |
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| Problems | |
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| References | |
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| Elements of Quality Assurance and Acceptance Sampling | |
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| Appendices | |
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| Probability Tables | |
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| Standard Normal Probabilities | |
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| CDF of the Binomial Distribution | |
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| Critical Values of t-Distribution at Confidence Level (1-[alpha]) = p | |
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| Critical Values of the x[superscript 2] Distribution at probability Level [alpha] | |
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| Critical Values of D[superscript alpha subscript n] at Significance Level [alpha] in the K-S Test | |
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| Critical Values of the Anderson-Darling Goodness-of-Fit Test | |
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| Combinatorial Formulas | |
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| The Basic Relation | |
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| The Binomial Coefficient | |
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| The Multinomial Coefficient | |
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| Stirling's Formula | |
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| Derivation of the Poisson Distribution | |
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| Index | |