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Probability, statistics, and decision for civil engineers
"This text covers the development of decision theory and related applications of probability. Extensive examples and illustrations cultivate students' appreciation for applications, including strength of materials, soil mechanics, construction planning, and water-resource design. Emphasis on fundamentals makes the material accessible to students trained in classical statistics and provides a brief introduction to probability. 1970 edition"--
Cover; Title Page; Copyright Page; Dedication; Preface; Contents; Introduction; Chapter 1 Data Reduction; 1.1 Graphical Displays; 1.2 Numerical Summaries; 1.3 Data Observed in Pairs; 1.4 Summary for Chapter 1; Chapter 2 Elements of Probability Theory; 2.1 Random Events; 2.1.1 Sample Space and Events; 2.1.2 Probability Measure; 2.1.3 Simple Probabilities of Events; 2.1.4 Summary; 2.2 Random Variables and Distributions; 2.2.1 Random Variables; 2.2.2 Jointly Distributed Random Variables; 2.3 Derived Distributions; 2.3.1 One-variable Transformations: Y = g(X).
2.3.2 Functions of Two Random Variables2.3.3 Elementary Simulation; 2.3.4 Summary; 2.4 Moments and Expectation; 2.4.1 Moments of a Random Variable; 2.4.2 Expectation of a Function of a Random Variable; 2.4.3 Expectation and Jointly Distributed Random Variables; 2.4.4 Approximate Moments and Distributions of Functions; 2.4.5 Summary; 2.5 Summary for Chapter 2; Chapter 3 Common Probabilistic Models; 3.1 Models from Simple Discrete Random Trials; 3.1.1 A Single Trial: The Bernoulli Distribution; 3.1.2 Repeated Trials: The Binomial Distribution.
3.1.3 Repeated Trials: The Geometric and Negative Binomial Distributions3.1.4 Summary; 3.2 Models from Random Occurrences; 3.2.1 Counting Events: The Poisson Distribution; 3.2.2 Time between Events: The Exponential Distribution; 3.2.3 Time to the kth Event: The Gamma Distribution; 3.2.4 Summary; 3.3 Models from Limiting Cases; 3.3.1 The Model of Sums: The Normal Distribution; 3.3.2 The Model of Products: The Lognormal Distribution; 3.3.3 The Model of Extremes: The Extreme Value Distributions; 3.3.4 Summary; 3.4 Additional Common Distributions.
3.4.1 The Equally Likely Model: The Rectangular or Uniform Distribution3.4.2 The Beta Distribution; 3.4.3 Some Normal Related Distributions: Chi-square, Chi, t, and F; 3.4.4 Summary; 3.5 Modified Distributions; 3.5.1 Shifted and Transformed Distributions; 3.5.2 Truncated and Censored Distributions; 3.5.3 Compound Distributions; 3.5.4 Summary; 3.6 Multivariate Models; 3.6.1 Counting Multiple Events: The Multinomial Distribution; 3.6.2 The Multivariate Normal Distribution; 3.6.3 Summary; 3.7 Markov Chains; 3.7.1 Simple Markov Chains; 3.7.2 Two-state Homogeneous Chains.
3.7.3 Multistate Markov Chains3.7.4 Summary; 3.8 Summary for Chapter 3; Chapter 4 Probabilistic Models and Observed Data; 4.1 Estimation of Model Parameters; 4.1.1 The Method of Moments; 4.1.2 The Properties of Estimators: Their First- and Second-order Moments; 4.1.3 The Distributions of Estimators and Confidence-interval Estimation; 4.1.4 The Method of Maximum Likelihood; 4.1.5 Summary; 4.2 Significance Testing; 4.2.1 Hypothesis Testing; 4.2.2 Some Common Hypothesis Tests; 4.2.3 Summary; 4.3 Statistical Analysis of Linear Models; 4.3.1 Linear Models.
Reprint of: New York : McGraw-Hill, 1970.
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Includes bibliographical references and index.
Benjamin, Jack R. (Jack Ralph), 1917-1998.