《國外電子與通信教材系列：概率、統計與隨機過程（第四版）（英文版）》從工程應用的角度，全面闡述概率、統計與隨機過程的基本理論及其應用。全書共11章，首先簡單介紹概率論，然后各章分別討論隨機變量、隨機變量的函數、均值與矩、隨機矢量、統計（包括參數估計和假設檢驗）、隨機序列、隨機過程基礎知識和深入探討，最后討論了統計信號處理中的相關應用。書中給出了大量電子和信息系統相關實例，每章給出了豐富的習題。
《國外電子與通信教材系列：概率、統計與隨機過程（第四版）（英文版）》適合作為電子信息類專業本科生和研究生的“隨機信號分析”或“隨機過程及其應用”課程的雙語教學教材，也可供從事相關技術領域研究的科技人員參考。
Preface
While significant changes have been made in the current edition from its predecessor, the authors have tried to keep the discussion at the same level of accessibly, that is, less mathematical than the measure theory approach but more rigorous than formula and recipe manuals.
It has been said that probability is hard to understand, not so much because of its mathematical underpinnings but because it produces many results that are counter intuitive. Among practically oriented students, Probability has many critics. Foremost among these are the ones who ask, “What do we need it for?” This criticism is easy to answer because future engineers and scientists will come to realize that almost every human endeavor involves making decisions in an uncertain or probabilistic environment. This is true for entire fields such as insurance, meteorology, urban planning, pharmaceuticals, and many more. Another, possibly more potent, criticism is, “What good is probability if the answers it furnishes are not certainties but just inferences and likelihoods?” The nswer here is that an immense amount of good planning and accurate predictions can be done even in the realm of uncertainty. Moreover, applied probability—often called statistics—does provide near certainties: witness the enormous success of political polling and prediction.
In previous editions, we have treaded lightly in the area of statistics and more heavily in the area of random processes and signal processing. In the electronic version of this book, graduate-level signal processing and advanced discussions of random processes are retained, along with new material on statistics. In the hard copy version of the book, we have dropped the chapters on applications to statistical signal processing and advanced topics in random
processes, as well as some introductory material on pattern recognition.
The present edition makes a greater effort to reach students with more expository examples and more detailed discussion. We have minimized the use of phrases such as,“it is easy to show ”,“it can be shown ”,“it is easy to see... ,”and the like. Also, we have tried to furnish examples from real-world issues such as the efficacy of drugs, the likelihood of contagion, and the odds of winning at gambling, as well as from digital communications, networks, and signals.
The other major change is the addition of two chapters on elementary statistics and its applications to real-world problems. The first of these deals with parameter estimation and the second with hypothesis testing. Many activities in engineering involve estimating parameters, for example, from estimating the strength of a new concrete formula to estimating the amount of signal traffic between computers. Likewise many engineering activities involve
making decisions in random environments, from deciding whether new drugs are effective to deciding the effectiveness of new teaching methods. The origin and applications of standard statistical tools such as the t-test, the Chi-square test, and the F-test are presented and discussed with detailed examples and end-of-chapter problems.
Finally, many self-test multiple-choice exams are now available for students at the book Web site. These exams were administered to senior undergraduate and graduate students at the Illinois Institute of Technology during the tenure of one of the authors who taught there from 1988 to 2006. The Web site also includes an extensive set of small MATLAB programs that illustrate the concepts of probability.
In summary then, readers familiar with the 3rd edition will see the following significant changes:
A new chapter on a branch of statistics called parameter estimation with many illustrative examples;
A new chapter on a branch of statistics called hypothesis testing with many illustrative examples;
A large number of new homework problems of varying degrees of difficulty to test the student’s mastery of the principles of statistics;
A large number of self-test, multiple-choice, exam questions calibrated to the material in various chapters
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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