概率、统计与随机过程 : 第4版

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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《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）》从工程应用的角度，全面阐述概率、统计与随机过程的基本理论及其应用。全书共11章，首先简单介绍概率论，然后各章分别讨论随机变量、随机变量的函数、均值与矩、随机矢量、统计（包括参数估计和假设检验）、随机序列、随机过程基础知识和深入探讨，最后讨论了统计信号处理中的相关应用。书中给出了大量电子和信息系统相关实例，每章给出了丰富的习题。

《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。