概率、統(tǒng)計與隨機過程

前言

　　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

內(nèi)容概要

　　《國外電子與通信教材系列：概率、統(tǒng)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(tǒng)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(shù)、均值與矩、隨機矢量、統(tǒng)計（包括參數(shù)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(tǒng)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(tǒng)相關實例，每章給出了豐富的習題。

書籍目錄

Preface 11Chapter1 Introduction to Probability 131.1 Introduction: Why Study Probability? 131.2 The Different Kinds of Probability 14Probability as Intuition 14Probability as the Ratio of Favorable to Total Outcomes (Classical Theory) 15Probability as a Measure of Frequency of Occurrence 16Probability Based on an Axiomatic Theory 171.3 Misuses, Miscalculations, and Paradoxes in Probability 191.4 Sets, Fields, and Events 20Examples of Sample Spaces 201.5 Axiomatic Definition of Probability 271.6 Joint, Conditional, and Total Probabilities; Independence 32Compound Experiments 351.7 Bayes’ Theorem and Applications 471.8 Combinatorics 50Occupancy Problems 54Extensions and Applications 581.9 Bernoulli Trials—Binomial and Multinomial Probability Laws 60Multinomial Probability Law 661.10 Asymptotic Behavior of the Binomial Law: The Poisson Law 691.11 Normal Approximation to the Binomial Law 75Summary 77Problems 78References 89Chapter2 Random Variables 912.1 Introduction 912.2 Definition of a Random Variable 922.3 Cumulative Distribution Function 95Properties of FX(x) 96Computation of FX(x) 972.4 Probability Density Function (pdf) 100Four Other Common Density Functions 107More Advanced Density Functions 1092.5 Continuous, Discrete, and Mixed Random Variables 112Some Common Discrete Random Variables 1142.6 Conditional and Joint Distributions and Densities 119Properties of Joint CDF FXY (x, y) 1302.7 Failure Rates 149Summary 153Problems 153References 161Additional Reading 161Chapter3 Functions of Random Variables 1633.1 Introduction 163Functions of a Random Variable (FRV): Several Views 1663.2 Solving Problems of the Type Y = g(X) 167General Formula of Determining the pdf of Y = g(X) 1783.3 Solving Problems of the Type Z = g(X, Y ) 1833.4 Solving Problems of the Type V = g(X, Y ), W = h(X, Y ) 205Fundamental Problem 205Obtaining fVW Directly from fXY 2083.5 Additional Examples 212Summary 217Problems 218References 226Additional Reading 226Chapter4 Expectation and Moments 2274.1 Expected Value of a Random Variable 227On the Validity of Equation 4.1-8 2304.2 Conditional Expectations 244Conditional Expectation as a Random Variable 2514.3 Moments of Random Variables 254Joint Moments 258Properties of Uncorrelated Random Variables 260Jointly Gaussian Random Variables 2634.4 Chebyshev and Schwarz Inequalities 267Markov Inequality 269The Schwarz Inequality 2704.5 Moment-Generating Functions 2734.6 Chernoff Bound 2764.7 Characteristic Functions 278Joint Characteristic Functions 285The Central Limit Theorem 2884.8 Additional Examples 293Summary 295Problems 296References 305Additional Reading 306Chapter5 Random Vectors 3075.1 Joint Distribution and Densities 3075.2 Multiple Transformation of Random Variables 3115.3 Ordered Random Variables 3145.4 Expectation Vectors and Covariance Matrices 3235.5 Properties of Covariance Matrices 326Whitening Transformation 3305.6 The Multidimensional Gaussian (Normal) Law 3315.7 Characteristic Functions of Random Vectors 340Properties of CF of Random Vectors 342The Characteristic Function of the Gaussian (Normal) Law 343Summary 344Problems 345References 351Additional Reading 351Chapter6 Statistics: Part 1 Parameter Estimation 3526.1 Introduction 352Independent, Identically, Observations 353Estimation of Probabilities 3556.2 Estimators 3586.3 Estimation of the Mean 360Properties of the Mean-Estimator Function (MEF) 361Procedure for Getting a δ-confidence Interval on the Mean of a NormalRandom Variable When σX Is Known 364Confidence Interval for the Mean of a Normal Distribution When σX Is NotKnown 364Procedure for Getting a δ-Confidence Interval Based on n Observations onthe Mean of a Normal Random Variable when σX Is Not Known 367Interpretation of the Confidence Interval 3676.4 Estimation of the Variance and Covariance 367Confidence Interval for the Variance of a Normal Randomvariable 369Estimating the Standard Deviation Directly 371Estimating the covariance 3726.5 Simultaneous Estimation of Mean and Variance 3736.6 Estimation of Non-Gaussian Parameters from Large Samples 3756.7 Maximum Likelihood Estimators 3776.8 Ordering, more on Percentiles, Parametric Versus Nonparametric Statistics 381The Median of a Population Versus Its Mean 383Parametric versus Nonparametric Statistics 384Confidence Interval on the Percentile 385Confidence Interval for the Median When n Is Large 3876.9 Estimation of Vector Means and Covariance Matrices 388Estimation of μ 389Estimation of the covariance K 3906.10 Linear Estimation of Vector Parameters 392Summary 396Problems 396References 400Additional Reading 401Chapter7 Statistics: Part 2 Hypothesis Testing 4027.1 Bayesian Decision Theory 4037.2 Likelihood Ratio Test 4087.3 Composite Hypotheses 414Generalized Likelihood Ratio Test (GLRT) 415How Do We Test for the Equality of Means of Two Populations? 420Testing for the Equality of Variances for Normal Populations:The F-test 424TestingWhether the Variance of a Normal Population Has a PredeterminedValue: 4287.4 Goodness of Fit 4297.5 Ordering, Percentiles, and Rank 435How Ordering is Useful in Estimating Percentiles and the Median 437Confidence Interval for the Median When n Is Large 440Distribution-free Hypothesis Testing: Testing If Two Population are theSame Using Runs 441Ranking Test for Sameness of Two Populations 444Summary 445Problems 445References 451Chapter8 Random Sequences 4538.1 Basic Concepts 454Infinite-length Bernoulli Trials 459Continuity of Probability Measure 464Statistical Specification of a Random Sequence 4668.2 Basic Principles of Discrete-Time Linear Systems 4838.3 Random Sequences and Linear Systems 4898.4 WSS Random Sequences 498Power Spectral Density 501Interpretation of the psd 502Synthesis of Random Sequences and Discrete-Time Simulation 505Decimation 508Interpolation 5098.5 Markov Random Sequences 512ARMA Models 515Markov Chains 5168.6 Vector Random Sequences and State Equations 5238.7 Convergence of Random Sequences 5258.8 Laws of Large Numbers 533Summary 538Problems 538References 553Chapter9 Random Processes 5559.1 Basic Definitions 5569.2 Some Important Random Processes 560Asynchronous Binary Signaling 560Poisson Counting Process 562Alternative Derivation of Poisson Process 567Random Telegraph Signal 569Digital Modulation Using Phase-Shift Keying 570Wiener Process or Brownian Motion 572Markov Random Processes 575Birth–Death Markov Chains 579Chapman–Kolmogorov Equations 583Random Process Generated from Random Sequences 5849.3 Continuous-Time Linear Systems with Random Inputs 584White Noise 5899.4 Some Useful Classifications of Random Processes 590Stationarity 5919.5 Wide-Sense Stationary Processes and LSI Systems 593Wide-Sense Stationary Case 594Power Spectral Density 596An Interpretation of the psd 598More on White Noise 602Stationary Processes and Differential Equations 6089.6 Periodic and Cyclostationary Processes 6129.7 Vector Processes and State Equations 618State Equations 620Summary 623Problems 623References 645Chapters 10 and 11 are available as Web chapters on the companionWeb site at www.pearsoninternationaleditions.com/stark.Chapter10 Advanced Topics in Random Processes 64710.1 Mean-Square (m.s.) Calculus 647Stochastic Continuity and Derivatives [10-1] 647Further Results on m.s. Convergence [10-1] 65710.2 Mean-Square Stochastic Integrals 66210.3 Mean-Square Stochastic Differential Equations 66510.4 Ergodicity [10-3] 67010.5 Karhunen–Lo`eve Expansion [10-5] 67710.6 Representation of Bandlimited and Periodic Processes 683Bandlimited Processes 683Bandpass Random Processes 686WSS Periodic Processes 689Fourier Series for WSS Processes 692Summary 694Appendix: Integral Equations 694Existence Theorem 695Problems 698References 711Chapter11 Applications to Statistical Signal Processing 71211.1 Estimation of Random Variables and Vectors 712More on the Conditional Mean 718Orthogonality and Linear Estimation 720Some Properties of the Operator ＆#710;E 72811.2 Innovation Sequences and Kalman Filtering 730Predicting Gaussian Random Sequences 734Kalman Predictor and Filter 736Error-Covariance Equations 74111.3 Wiener Filters for Random Sequences 745Unrealizable Case (Smoothing) 746Causal Wiener Filter 748“A01_STAR2288_04_PIE_FM” — 2011/9/16 — 17:15 — page 9Contents 911.4 Expectation-Maximization Algorithm 750Log-likelihood for the Linear Transformation 752Summary of the E-M algorithm 754E-M Algorithm for Exponential ProbabilityFunctions 755Application to Emission Tomography 756Log-likelihood Function of Complete Data 758E-step 759M-step 76011.5 Hidden Markov Models (HMM) 761Specification of an HMM 763Application to Speech Processing 765Efficient Computation of P[E|M] with a RecursiveAlgorithm 766Viterbi Algorithm and the Most Likely State Sequencefor the Observations 76811.6 Spectral Estimation 771The Periodogram 772Bartlett’s Procedure---Averaging Periodograms 774Parametric Spectral Estimate 779Maximum Entropy Spectral Density 78111.7 Simulated Annealing 784Gibbs Sampler 785Noncausal Gauss–Markov Models 786Compound Markov Models 790Gibbs Line Sequence 791Summary 795Problems 795References 800Appendix A Review of Relevant Mathematics A-1A.1 Basic Mathematics A-1Sequences A-1Convergence A-2Summations A-3Z-Transform A-3A.2 Continuous Mathematics A-4Definite and Indefinite Integrals A-5Differentiation of Integrals A-6Integration by Parts A-7Completing the Square A-7Double Integration A-8Functions A-8A.3 Residue Method for Inverse Fourier Transformation A-10Fact A-11Inverse Fourier Transform for psd of Random Sequence A-13A.4 Mathematical Induction A-17References A-17Appendix B Gamma and Delta Functions B-1B.1 Gamma Function B-1B.2 Incomplete Gamma Function B-2B.3 Dirac Delta Function B-2References B-5Appendix C Functional Transformations and Jacobians C-1C.1 Introduction C-1C.2 Jacobians for n = 2 C-2C.3 Jacobian for General n C-4Appendix D Measure and Probability D-1D.1 Introduction and Basic Ideas D-1Measurable Mappings and Functions D-3D.2 Application of Measure Theory to Probability D-3Distribution Measure D-4Appendix E Sampled Analog Waveforms and Discrete-time Signals E-1Appendix F Independence of Sample Mean and Variance for Normal Random Variables F-1Appendix G Tables of Cumulative Distribution Functions: the Normal, Student t, Chi-square, and F G-1Index I-1

編輯推薦

斯塔克、伍茲編著的《概率統(tǒng)計與隨機過程（第4版英文版）》從工程應用的角度，全面闡述概率、統(tǒng)計與隨機過程的基本理論及其應用。適合作為電子信息類專業(yè)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。

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