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| Preface | |
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| Preface to the First Edition | |
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| Basic Probability Theory | |
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| Introduction | |
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| Sample Spaces and Events | |
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| The Axioms of Probability | |
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| Finite Sample Spaces and Combinatorics | |
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| Combinatorics | |
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| Conditional Probability and Independence | |
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| Independent Events | |
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| The Law of Total Probability and Bayes' Formula | |
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| Bayes' Formula | |
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| Genetics and Probability | |
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| Recursive Methods | |
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| Problems | |
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| Random Variables | |
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| Introduction | |
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| Discrete Random Variables | |
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| Continuous Random Variables | |
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| The Uniform Distribution | |
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| Functions of Random Variables | |
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| Expected Value and Variance | |
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| The Expected Value of a Function of a Random Variable | |
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| Variance of a Random Variable | |
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| Special Discrete Distributions | |
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| Indicators | |
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| The Binomial Distribution | |
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| The Geometric Distribution | |
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| The Poisson Distribution | |
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| The Hypergeometric Distribution | |
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| Describing Data Sets | |
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| The Exponential Distribution | |
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| The Normal Distribution | |
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| Other Distributions | |
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| The Lognormal Distribution | |
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| The Gamma Distribution | |
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| The Cauchy Distribution | |
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| Mixed Distributions | |
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| Location Parameters | |
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| The Failure Rate Function | |
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| Uniqueness of the Failure Rate Function | |
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| Problems | |
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| Joint Distributions | |
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| Introduction | |
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| The Joint Distribution Function | |
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| Discrete Random Vectors | |
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| Jointly Continuous Random Vectors | |
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| Conditional Distributions and Independence | |
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| Independent Random Variables | |
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| Functions of Random Vectors | |
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| Real-Valued Functions of Random Vectors | |
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| The Expected Value and Variance of a Sum | |
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| Vector-Valued Functions of Random Vectors | |
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| Conditional Expectation | |
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| Conditional Expectation as a Random Variable | |
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| Conditional Expectation and Prediction | |
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| Conditional Variance | |
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| Recursive Methods | |
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| Covariance and Correlation | |
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| The Correlation Coefficient | |
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| The Bivariate Normal Distribution | |
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| Multidimensional Random Vectors | |
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| Order Statistics | |
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| Reliability Theory | |
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| The Multinomial Distribution | |
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| The Multivariate Normal Distribution | |
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| Convolution | |
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| Generating Functions | |
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| The Probability Generating Function | |
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| The Moment Generating Function | |
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| The Poisson Process | |
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| Thinning and Superposition | |
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| Problems | |
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| Limit Theorems | |
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| Introduction | |
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| The Law of Large Numbers | |
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| The Central Limit Theorem | |
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| The Delta Method | |
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| Convergence in Distribution | |
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| Discrete Limits | |
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| Continuous Limits | |
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| Problems | |
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| Simulation | |
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| Introduction | |
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| Random Number Generation | |
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| Simulation of Discrete Distributions | |
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| Simulation of Continuous Distributions | |
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| Miscellaneous | |
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| Problems | |
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| Statistical Inference | |
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| Introduction | |
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| Point Estimators | |
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| Estimating the Variance | |
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| Confidence Intervals | |
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| Confidence Interval for the Mean in the Normal Distribution with Known Variance | |
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| Confidence Interval for an Unknown Probability | |
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| One-Sided Confidence Intervals | |
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| Estimation Methods | |
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| The Method of Moments | |
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| Maximum Likelihood | |
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| Evaluation of Estimators with Simulation | |
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| Bootstrap Simulation | |
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| Hypothesis Testing | |
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| Large Sample Tests | |
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| Test for an Unknown Probability | |
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| Further Topics in Hypothesis Testing | |
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| P-Values | |
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| Data Snooping | |
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| The Power of a Test | |
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| Multiple Hypothesis Testing | |
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| Goodness of Fit | |
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| Goodness-of-Fit Test for Independence | |
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| Fisher's Exact Test | |
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| Bayesian Statistics | |
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| Noninformative priors | |
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| Credibility Intervals | |
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| Nonparametric Methods | |
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| Nonparametric Hypothesis Testing | |
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| Comparing Two Samples | |
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| Nonparametric Confidence Intervals | |
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| Problems | |
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| Linear Models | |
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| Introduction | |
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| Sampling Distributions | |
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| Single Sample Inference | |
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| Inference for the Variance | |
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| Inference for the Mean | |
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| Comparing Two Samples | |
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| Inference about Means | |
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| Inference about Variances | |
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| Analysis of Variance | |
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| One-Way Analysis of Variance | |
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| Multiple Comparisons: Tukey's Method | |
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| Kruskal-Wallis Test | |
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| Linear Regression | |
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| Prediction | |
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| Goodness of Fit | |
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| The Sample Correlation Coefficient | |
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| Spearman's Correlation Coefficient | |
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| The General Linear Model | |
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| Problems | |
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| Stochastic Processes | |
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| Introduction | |
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| Discrete-Time Markov Chains | |
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| Time Dynamics of a Markov Chain | |
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| Classification of States | |
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| Stationary Distributions | |
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| Convergence to the Stationary Distribution | |
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| Random Walks and Branching Processes | |
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| The Simple Random Walk | |
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| Multidimensional Random Walks | |
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| Branching Processes | |
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| Continuous-Time Markov Chains | |
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| Stationary Distributions and Limit Distributions | |
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| Birth-Death Processes | |
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| Queueing Theory | |
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| Further Properties of Queueing Systems | |
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| Martingales | |
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| Martingale Convergence | |
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| Stopping Times | |
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| Renewal Processes | |
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| Asymptotic Properties | |
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| Brownian Motion | |
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| Hitting Times | |
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| Variations of the Brownian Motion | |
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| Problems | |
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| Tables | |
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| Answers to Selected Problems | |
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| Further Reading | |
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| Index | |