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| Role of Probability in Engineering | |
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| Introduction | |
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| Uncertainty in Real-World Information | |
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| Uncertainty Associated with Randomness | |
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| Uncertainty Associated with Imperfect Modeling and Estimation | |
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| Design and Decision-Making Under Uncertainty | |
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| Planning and Design of Airport Pavement | |
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| Hydrologic Design | |
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| Design of Structures and Machines | |
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| Geotechnical Design | |
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| Construction Planning and Management | |
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| Photogrammetric, Geodetic, and Surveying Measurements | |
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| Control and Standards | |
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| Concluding Remarks | |
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| Basic Probability Concepts | |
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| Events and Probability | |
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| Characteristics of Probability Problems | |
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| Calculation of Probability | |
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| Elements of Set Theory | |
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| Definitions | |
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| Combination of Events | |
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| Operational Rules | |
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| Mathematics of Probability | |
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| Basic Axioms of Probability Addition Rule | |
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| Conditional Probability Multiplication Rule | |
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| Theorem of Total Probability | |
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| Bayes' Theorem | |
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| Concluding Remarks Problems | |
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| Analytical Models of Random Phenomena | |
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| 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 Normal Distribution | |
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| The Logarithmic Normal Distribution | |
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| 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 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 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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| Conditional Mean and Variance | |
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| Concluding Remarks Problems | |
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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 Single Random Variable | |
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| Function of Multiple Random Variables | |
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| Moments of Functions of Random Variables | |
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| Introduction | |
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| Mean and Variance of a Linear Function | |
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| Product of Independent Variates | |
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| Mean and Variance of a General Function | |
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| Concluding Remarks Problems | |
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| Estimating Parameters from Observational Data | |
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| The Role of Statistical Inference in Engineering | |
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| Inherent Variability and Estimation Error | |
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| Classical Approach to Estimation of Parameters | |
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| Random Sampling and Point Estimation | |
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| Interval Estimation of the Mean | |
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| Problems of Measurement Theory | |
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| Interval Estimation of the Variance | |
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| Estimation of Proportion | |
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| Concluding Remarks Problems | |
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| Empirical Determination of Distribution Models | |
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| Introduction | |
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| Probability Paper | |
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| The Normal Probability Paper | |
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| The Log-Normal Probability Paper | |
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| Construction of General Probability Paper | |
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| Testing Validity of Assumed Distribution | |
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| Chi-Square Test for Distribution | |
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| Kolmogorov-Smirnov Test for Distribution | |
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| Concluding Remarks Problems | |
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| Regression and Correlation Analyses | |
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| Basic Formulation of Linear Regression | |
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| Regression with Constant Variance | |
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| 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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| Correlation Analysis | |
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| Estimation of Correlation Coefficient | |
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| Concluding Remarks Problems | |
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| The Bayesian Approach | |
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| Introduction | |
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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 Bayesian Up-dating Process | |
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| Bayesian Concepts in Sampling Theory | |
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| General Formulation | |
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| Sampling from Normal Population | |
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| Error in Estimation | |
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| Use of Conjugate Distributions | |
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| Concluding Remarks Problems | |
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| Elements of Quality Assurance and Acceptance Sampling | |
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| Acceptance Sampling by Attributes | |
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| The Operating Characteristic (OC) Curve | |
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| The Success Run | |
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| The Average Outgoing Quality Curve | |
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| Acceptance Sampling by Variables | |
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| Average Quality Criterion, sigma Known | |
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| Average Quality Criterion, sigma Unknown | |
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| Fraction Defective Criterion | |
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| Multiple-Stage Sampling | |
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| Concluding Remarks Problems | |
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| Probability Tables | |
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| Table of Standard Normal Probability | |
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| p-Percentile Values of the t-Distribution | |
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| p-Percentile Values of the x 2 -Distribution | |
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| Critical Values of D alpha; in the Kolmogorov-Smirnov Test | |
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| Combinatorial Formulas | |
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| Derivation of the Poisson Distribution | |
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| References | |
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| Index | |