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| Preface | |
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| Introduction | |
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| Organization of Text | |
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| Probability Tables and Computer Software | |
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| Prerequisites | |
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| Probability and Random Variables | |
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| Basic Probability Concepts | |
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| Elements of Set Theory | |
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| Set Operations | |
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| Sample Space and Probability Measure | |
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| Axioms of Probability | |
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| Assignment of Probability | |
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| Statistical Independence | |
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| Conditional Probability | |
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| Reference | |
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| Further Reading | |
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| Problems | |
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| Random Variables and Probability Distributions | |
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| Random Variables | |
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| Probability Distributions | |
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| Probability Distribution Function | |
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| Probability Mass Function for Discrete Random Variables | |
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| Probability Density Function for Continuous Random Variables | |
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| Mixed-Type Distribution | |
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| Two or More Random Variables | |
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| Joint Probability Distribution Function | |
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| Joint Probability Mass Function | |
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| Joint Probability Density Function | |
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| Conditional Distribution and Independence | |
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| Further Reading and Comments | |
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| Problems | |
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| Expectations and Moments | |
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| Moments of a Single Random Variable | |
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| Mean, Median, and Mode | |
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| Central Moments, Variance, and Standard Deviation | |
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| Conditional Expectation | |
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| Chebyshev Inequality | |
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| Moments of Two or More Random Variables | |
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| Covariance and Correlation Coefficient | |
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| Schwarz Inequality | |
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| The Case of Three or More Random Variables | |
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| Moments of Sums of Random Variables | |
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| Characteristic Functions | |
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| Generation of Moments | |
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| Inversion Formulae | |
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| Joint Characteristic Functions | |
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| Further Reading and Comments | |
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| Problems | |
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| Functions of Random Variables | |
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| Functions of One Random Variable | |
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| Probability Distribution | |
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| Moments | |
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| Functions of Two or More Random Variables | |
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| Sums of Random Variables | |
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| m Functions of n Random Variables | |
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| Reference | |
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| Problems | |
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| Some Important Discrete Distributions | |
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| Bernoulli Trials | |
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| Binomial Distribution | |
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| Geometric Distribution | |
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| Negative Binomial Distribution | |
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| Multinomial Distribution | |
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| Poisson Distribution | |
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| Spatial Distributions | |
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| The Poisson Approximation to the Binomial Distribution | |
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| Summary | |
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| Further Reading | |
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| Problems | |
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| Some Important Continuous Distributions | |
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| Uniform Distribution | |
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| Bivariate Uniform Distribution | |
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| Gaussian or Normal Distribution | |
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| The Central Limit Theorem | |
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| Probability Tabulations | |
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| Multivariate Normal Distribution | |
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| Sums of Normal Random Variables | |
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| Lognormal Distribution | |
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| Probability Tabulations | |
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| Gamma and Related Distributions | |
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| Exponential Distribution | |
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| Chi-Squared Distribution | |
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| Beta and Related Distributions | |
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| Probability Tabulations | |
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| Generalized Beta Distribution | |
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| Extreme-Value Distributions | |
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| Type-I Asymptotic Distributions of Extreme Values | |
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| Type-II Asymptotic Distributions of Extreme Values | |
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| Type-III Asymptotic Distributions of Extreme Values | |
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| Summary | |
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| References | |
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| Further Reading and Comments | |
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| Problems | |
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| Statistical Inference, Parameter Estimation, and Model Verification | |
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| Observed Data and Graphical Representation | |
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| Histogram and Frequency Diagrams | |
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| References | |
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| Problems | |
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| Parameter Estimation | |
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| Samples and Statistics | |
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| Sample Mean | |
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| Sample Variance | |
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| Sample Moments | |
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| Order Statistics | |
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| Quality Criteria for Estimates | |
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| Unbiasedness | |
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| Minimum Variance | |
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| Consistency | |
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| Sufficiency | |
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| Methods of Estimation | |
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| Point Estimation | |
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| Interval Estimation | |
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| References | |
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| Further Reading and Comments | |
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| Problems | |
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| Model Verification | |
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| Preliminaries | |
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| Type-I and Type-II Errors | |
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| Chi-Squared Goodness-of-Fit Test | |
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| The Case of Known Parameters | |
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| The Case of Estimated Parameters | |
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| Kolmogorov-Smirnov Test | |
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| References | |
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| Further Reading and Comments | |
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| Problems | |
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| Linear Models and Linear Regression | |
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| Simple Linear Regression | |
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| Least Squares Method of Estimation | |
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| Properties of Least-Square Estimators | |
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| Unbiased Estimator for [sigma superscript 2] | |
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| Confidence Intervals for Regression Coefficients | |
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| Significance Tests | |
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| Multiple Linear Regression | |
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| Least Squares Method of Estimation | |
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| Other Regression Models | |
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| Reference | |
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| Further Reading | |
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| Problems | |
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| Tables | |
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| Binomial Mass Function | |
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| Poisson Mass Function | |
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| Standardized Normal Distribution Function | |
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| Student's t Distribution with n Degrees of Freedom | |
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| Chi-Squared Distribution with n Degrees of Freedom | |
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| D[subscript 2] Distribution with Sample Size n | |
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| References | |
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| Computer Software | |
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| Answers to Selected Problems | |
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| Chapter 2 | |
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| Chapter 3 | |
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| Chapter 4 | |
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| Chapter 5 | |
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| Chapter 6 | |
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| Chapter 7 | |
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| Chapter 8 | |
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| Chapter 9 | |
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| Chapter 10 | |
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| Chapter 11 | |
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| Subject Index | |