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| Preface | |
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| Probability and Random Variables | |
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| The Meaning of Probability | |
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| Introduction | |
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| The Definitions | |
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| Probability and Induction | |
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| Causality Versus Randomness | |
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| The Axioms of Probability | |
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| Set Theory | |
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| Probability Space | |
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| Conditional Probability | |
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| Problems | |
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| Repeated Trials | |
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| Combined Experiments | |
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| Bernoulli Trials | |
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| Bernoulli's Theorem and Games of Chance | |
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| Problems | |
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| The Concept of a Random Variable | |
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| Introduction | |
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| Distribution and Density Functions | |
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| Specific Random Variables | |
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| Conditional Distributions | |
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| Asymptotic Approximations for Binomial Random Variable | |
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| Problems | |
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| Functions of One Random Variable | |
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| The Random Variable g(x) | |
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| The Distribution of g(x) | |
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| Mean and Variance | |
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| Moments | |
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| Characteristic Functions | |
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| Problems | |
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| Two Random Variables | |
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| Bivariate Distributions | |
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| One Function of Two Random Variables | |
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| Two Functions of Two Random Variables | |
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| Joint Moments | |
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| Joint Characteristic Functions | |
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| Conditional Distributions | |
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| Conditional Expected Values | |
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| Problems | |
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| Sequences of Random Variables | |
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| General Concepts | |
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| Conditional Densities, Characteristic Functions, and Normality | |
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| Mean Square Estimation | |
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| Stochastic Convergence and Limit Theorems | |
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| Random Numbers: Meaning and Generation | |
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| Problems | |
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| Statistics | |
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| Introduction | |
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| Estimation | |
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| Parameter Estimation | |
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| Hypothesis Testing | |
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| Problems | |
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| Stochastic Processes | |
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| General Concepts | |
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| Definitions | |
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| Systems with Stochastic Inputs | |
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| The Power Spectrum | |
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| Discrete-Time Processes | |
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| Continuity, Differentiation, Integration | |
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| Shift Operators and Stationary Processes | |
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| Problems | |
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| Random Walks and Other Applications | |
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| Random Walks | |
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| Poisson Points and Shot Noise | |
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| Modulation | |
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| Cyclostationary Processes | |
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| Bandlimited Processes and Sampling Theory | |
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| Deterministic Signals in Noise | |
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| Bispectra and System Identification | |
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| The Poisson Sum Formula | |
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| The Schwarz Inequality | |
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| Problems | |
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| Spectral Representation | |
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| Factorization and Innovations | |
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| Finite-Order Systems and State Variables | |
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| Fourier Series and Karhunen-Loeve Expansions | |
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| Spectral Representation of Random Processes | |
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| Problems | |
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| Spectrum Estimation | |
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| Ergodicity | |
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| Spectrum Estimation | |
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| Extrapolation and System Identification | |
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| The General Class of Extrapolating Spectra and Youla's Parametrization | |
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| Minimum-Phase Functions | |
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| All-Pass Functions | |
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| Problems | |
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| Mean Square Estimation | |
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| Introduction | |
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| Prediction | |
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| Filtering and Prediction | |
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| Kalman Filters | |
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| Problems | |
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| Entropy | |
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| Introduction | |
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| Basic Concepts | |
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| Random Variables and Stochastic Processes | |
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| The Maximum Entropy Method | |
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| Coding | |
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| Channel Capacity | |
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| Problems | |
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| Markov Chains | |
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| Introduction | |
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| Higher Transition Probabilities and the Chapman-Kolmogorov Equation | |
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| Classification of States | |
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| Stationary Distributions and Limiting Probabilities | |
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| Transient States and Absorption Probabilities | |
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| Branching Processes | |
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| Mixed Type Population of Constant Size | |
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| Structure of Periodic Chains | |
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| Problems | |
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| Markov Processes and Queueing Theory | |
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| Introduction | |
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| Markov Processes | |
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| Queueing Theory | |
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| Networks of Queues | |
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| Problems | |
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| Bibliography | |
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| Index | |