内容

目次

Preface. Chapter 1: Sets, Fields, and Events. 1.1 Set Definitions.1.2 Set Operations. 1.3 Set Algebras, Fields, and Events. Chapter 2:Probability Space and Axioms. 2.1 Probability Space. 2.2 ConditionalProbability. 2.3 Independence. 2.4 Total Probability and Bayes'Theorem. Chapter 3: Basic Combinatorics. 3.1 Basic Counting Principles.3.2 Permutations. 3.3 Combinations. Chapter 4: DiscreteDistributions. 4.1 Bernoulli Trials. 4.2 Binomial Distribution. 4.3Multinomial Distribution. 4.4 Geometric Distribution. 4.5 NegativeBinomial Distribution. 4.6 Hypergeometric Distribution. 4.7 PoissonDistribution. 4.8 Logarithmic Distribution. 4.9 Summary of DiscreteDistributions. Chapter 5: Random Variables. 5.1 Definition of RandomVariables. 5.2 Determination of Distribution and Density Functions. 5.3Properties of Distribution and Density Functions. 5.4 DistributionFunctions from Density Functions. Chapter 6: Continuous Random Variablesand Basic Distributions. 6.1 Introduction. 6.2 Uniform Distribution.6.3 Exponential Distribution. 6.4 Normal or Gaussian Distribution.Chapter 7: Other Continuous Distributions. 7.1 Introduction. 7.2Triangular Distribution. 7.3 Laplace Distribution. 7.4 ErlangDistribution. 7.5 Gamma Distribution. 7.6 Weibull Distribution. 7.7Chi-Square Distribution. 7.8 Chi and Other Allied Distributions. 7.9Student-t Density. 7.10 Snedecor F Distribution. 7.11 LognormalDistribution. 7.12 Beta Distribution. 7.13 Cauchy Distribution. 7.14Pareto Distribution. 7.15 Gibbs Distribution. 7.16 Mixed Distributions.7.17 Summary of Distributions of Continuous Random Variables. Chapter8: Conditional Densities and Distributions. 8.1 Conditional Distributionand Density for P(A) = 0. 8.2 Conditional Distribution and Density forP(A) 0. 8.3 Total Probability and Bayes' Theorem for Densities.Chapter 9: Joint Densities and Distributions. 9.1 Joint DiscreteDistribution Functions. 9.2 Joint Continuous Distribution Functions 9.3Bivariate Gaussian Distributions. Chapter 10: Moments and ConditionalMoments. 10.1 Expectations. 10.2 Variance. 10.3 Means and Variancesof Some Distributions. 10.4 Higher-Order Moments. 10.5 BivariateGaussian. Chapter 11: Characteristic Functions and Generating Functions.11.1 Characteristic Functions. 11.2 Examples of Characteristic Functions.11.3 Generating Functions. 11.4 Examples of Generating Functions.11.5 Moment Generating Functions. 11.6 Cumulant Generating Functions.11.7 Table of Means and Variances. Chapter 12: Functions of a SingleRandom Variable. 12.1 Random Variable g(X). 12.2 Distribution of Y =g(X ). 12.3 Direct Determination of Density fY (y) from fX(x). 12.4Inverse Problem: Finding g(x) Given fX(x) and fY (y). 12.5 Moments of aFunction of a Random Variable. Chapter 13: Functions of Multiple RandomVariables. 13.1 Function of Two Random Variables, Z = g(X,Y ). 13.2 TwoFunctions of Two Random Variables, Z = g(X,Y ), W = h(X,Y ). 13.3 DirectDetermination of Joint Density fZW(z,w ) from fXY(x,y). 13.4 Solving Z =g(X,Y ) Using an Auxiliary Random Variable. 13.5 Multiple Functions ofRandom Variables. Chapter 14: Inequalities, Convergences, and LimitTheorems. 14.1 Degenerate Random Variables. 14.2 Chebyshev and AlliedInequalities. 14.3 Markov Inequality. 14.4 Chernoff Bound. 14.5Cauchy-Schwartz Inequality. 14.6 Jensen's Inequality. 14.7 ConvergenceConcepts. 14.8 Limit Theorems. Chapter 15: Computer Methods forGenerating Random Variates. 15.1 Uniform-Distribution Random Variates.15.2 Histograms. 15.3 Inverse Transformation Techniques. 15.4Convolution Techniques. 15.5 Acceptance-Rejection Techniques. Chapter16: Elements of Matrix Algebra. 16.1 Basic Theory of Matrices. 16.2Eigenvalues and Eigenvectors of Matrices. 16.3 Vectors and MatrixDifferentiations. 16.4 Block Matrices. Chapter 17: Random Vectors andMean-Square Estimation. 17.1 Distributions and Densities. 17.2 Momentsof Random Vectors. 17.3 Vector Gaussian Random Variables. 17.4Diagonalization of Covariance Matrices. 17.5 Simultaneous Diagonalizationof Covariance Matrices. 17.6 Linear Estimation of Vector Variables.Chapter 18: Estimation Theory. 18.1 Criteria of Estimators. 18.2Estimation of Random Variables. 18.3 Estimation of Parameters (PointEstimation). 18.4 Interval Estimation (Confidence Intervals). 18.5Hypothesis Testing (Binary). 18.6 Bayesian Estimation. Chapter 19:Random Processes. 19.1 Basic Definitions. 19.2 Stationary RandomProcesses. 19.3 Ergodic Processes. 19.4 Estimation of Parameters ofRandom Processes. 19.5 Power Spectral Density. Chapter 20:Classification of Random Processes. 20.1 Specifications of RandomProcesses. 20.2 Poisson Process. 20.3 Binomial Process. 20.4Independent Increment Process. 20.5 Random-Walk Process. 20.6 GaussianProcess. 20.7 Wiener Process (Brownian Motion). 20.8 Markov Process.20.9 Markov Chain. 20.10 Martingale Process. 20.11 Periodic RandomProcess. 20.12 Aperiodic Random Process (Karhunen-Loeve Expansion).Chapter 21: Random Processes and Linear Systems. 21.1 Review of LinearSystems. 21.2 Random Processes through Linear Systems. 21.3 LinearFilters. 21.4 Bandpass Stationary Random Processes. Chapter 22: Weinerand Kalman Filters. 22.1 Review of Orthogonality Principle. 22.2 WienerFiltering. 22.3 Discrete Kalman Filter. 22.4 Continuous Kalman Filter.Chapter 23: Probabilistic Methods in Transmission Tomography. 23.1Introduction. 23.2 Stochastic Model. 23.3 Stochastic EstimationAlgorithm. 23.4 Prior Distribution P(M). 23.5 Computer Simulation.23.6 Results and Conclusions. 23.7 Discussion of Results. 23.8References for Chapter 23. APPENDIXES. A: A Fourier Transform Tables.B: Cumulative Gaussian Tables. C: Inverse Cumulative Gaussian Tables.D: Inverse Chi-Square Tables. E: Inverse Student-t Tables. F:Cumulative Poisson Distribution. G: Cumulative Binomial Distribution.References. Index.