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| 《国外电子与通信教材系列：概率、统计与随机过程（第四版）（英文版）》适合作为电子信息类专业本科生和研究生的“随机信号分析”或“随机过程及其应用”课程的双语教学教材，也可供从事相关技术领域研究的科技人员参考。 |
| Preface Chapter 1 Introduction to Probability 1.1 Introduction: Why Study Probability? 1.2 The Different Kinds of Probability Probability as Intuition Probability as the Ratio of Favorable to Total Outcomes (Classical Theory) Probability as a Measure of Frequency of Occurrence Probability Based on an Axiomatic Theory 1.3 Misuses, Miscalculations, and Paradoxes in Probability 1.4 Sets, Fields, and Events Examples of Sample Spaces 1.5 Axiomatic Definition of Probability 1.6 Joint, Conditional, and Total Probabilities; Independence Compound Experiments 1.7 Bayes' Theorem and Applications 1.8 Combinatorics Occupancy Problems Extensions and Applications 1.9 Bernoulli Trials-Binomial and Multinomial Probability Laws Multinomial Probability Law 1.10 Asymptotic Behavior of the Binomial Law: The Poisson Law 1.11 Normal Approximation to the Binomial Law Summary Problems References Chapter 2 Random Variables 2.1 Introduction 2.2 Definition of a Random Variable 2.3 Cumulative Distribution Function Properties of FX(x) Computation of FX(x) 2.4 Probability Density Function (pdf) Four Other Common Density Functions More Advanced Density Functions 2.5 Continuous, Discrete, and Mixed Random Variables Some Common Discrete Random Variables 2.6 Conditional and Joint Distributions and Densities Properties of Joint CDF FXY (x, y) 2.7 Failure Rates Summary Problems References Additional Reading Chapter 3 Functions of Random Variables 3.1 Introduction Functions of a Random Variable (FRV): Several Views 3.2 Solving Problems of the Type Y= g(X) General Formula of Determining the pdf of Y= g(X) 3.3 Solving Problems of the Type Z= g(X, Y ) 3.4 Solving Problems of the Type V= g(X, Y ), W= h(X, Y ) Fundamental Problem Obtaining fVW Directly from fXY 3.5 Additional Examples Summary Problems References Additional Reading Chapter 4 Expectation and Moments 4.1 Expected Value of a Random Variable On the Validity of Equation 4.1- 4.2 Conditional Expectations Conditional Expectation as a Random Variable 4.3 Moments of Random Variables Joint Moments Properties of Uncorrelated Random Variables Jointly Gaussian Random Variables 4.4 Chebyshev and Schwarz Inequalities Markov Inequality The Schwarz Inequality 4.5 Moment-Generating Functions 4.6 Chernoff Bound 4.7 Characteristic Functions Joint Characteristic Functions The Central Limit Theorem 4.8 Additional Examples Summary Problems References Additional Reading Chapter 5 Random Vectors 5.1 Joint Distribution and Densities 5.2 Multiple Transformation of Random Variables 5.3 Ordered Random Variables 5.4 Expectation Vectors and Covariance Matrices 5.5 Properties of Covariance Matrices Whitening Transformation 5.6 The Multidimensional Gaussian (Normal) Law 5.7 Characteristic Functions of Random Vectors Properties of CF of Random Vectors The Characteristic Function of the Gaussian (Normal) Law Summary Problems References Additional Reading Chapter 6 Statistics: Part 1 Parameter Estimation 6.1 Introduction Independent, Identically, Observations Estimation of Probabilities 6.2 Estimators 6.3 Estimation of the Mean …… |
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