{"product_id":"probability-and-random-processes-isbn-9781118923139","title":"Probability and Random Processes","description":"\u003cp\u003e\u003cb\u003eThe second edition enhanced with new chapters, figures, and appendices to cover the new developments in applied mathematical functions\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThis book examines the topics of applied mathematical functions to problems that engineers and researchers solve daily in the course of their work. The text covers set theory, combinatorics, random variables, discrete and continuous probability, distribution functions, convergence of random variables, computer generation of random variates, random processes and stationarity concepts with associated autocovariance and cross covariance functions, estimation theory and Wiener and Kalman filtering ending with two applications of probabilistic methods. Probability tables with nine decimal place accuracy and graphical Fourier transform tables are included for quick reference. The author facilitates understanding of probability concepts for both students and practitioners by presenting over 450 carefully detailed figures and illustrations, and over 350 examples with every step explained clearly and some with multiple solutions.\u003c\/p\u003e \u003cp\u003eAdditional features of the second edition of \u003ci\u003eProbability and Random Processes\u003c\/i\u003e are:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eUpdated chapters with new sections on Newton-Pepys’ problem; Pearson, Spearman, and Kendal correlation coefficients; adaptive estimation techniques; birth and death processes; and renewal processes with generalizations\u003c\/li\u003e \u003cli\u003eA new chapter on Probability Modeling in Teletraffic Engineering written by Kavitha Chandra\u003c\/li\u003e \u003cli\u003eAn eighth appendix examining the computation of the roots of discrete probability-generating functions\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eWith new material on theory and applications of probability, \u003ci\u003eProbability and Random Processes, Second Edition\u003c\/i\u003e is a thorough and comprehensive reference for commonly occurring problems in probabilistic methods and their applications.\u003c\/p\u003e \u003cp\u003ePreface for the Second Edition xii\u003c\/p\u003e \u003cp\u003ePreface for the First Edition xiv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Sets, Fields, and Events 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Set Definitions 1\u003c\/p\u003e \u003cp\u003e1.2 Set Operations 2\u003c\/p\u003e \u003cp\u003e1.3 Set Algebras, Fields, and Events 5\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Probability Space and Axioms 7\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Probability Space 7\u003c\/p\u003e \u003cp\u003e2.2 Conditional Probability 9\u003c\/p\u003e \u003cp\u003e2.3 Independence 11\u003c\/p\u003e \u003cp\u003e2.4 Total Probability and Bayes’ Theorem 12\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Basic Combinatorics 16\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Basic Counting Principles 16\u003c\/p\u003e \u003cp\u003e3.2 Permutations 16\u003c\/p\u003e \u003cp\u003e3.3 Combinations 18\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Discrete Distributions 23\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Bernoulli Trials 23\u003c\/p\u003e \u003cp\u003e4.2 Binomial Distribution 23\u003c\/p\u003e \u003cp\u003e4.3 Multinomial Distribution 26\u003c\/p\u003e \u003cp\u003e4.4 Geometric Distribution 26\u003c\/p\u003e \u003cp\u003e4.5 Negative Binomial Distribution 27\u003c\/p\u003e \u003cp\u003e4.6 Hypergeometric Distribution 28\u003c\/p\u003e \u003cp\u003e4.7 Poisson Distribution 30\u003c\/p\u003e \u003cp\u003e4.8 Newton–Pepys Problem and its Extensions 33\u003c\/p\u003e \u003cp\u003e4.9 Logarithmic Distribution 40\u003c\/p\u003e \u003cp\u003e4.9.1 Finite Law (Benford’s Law) 40\u003c\/p\u003e \u003cp\u003e4.9.2 Infinite Law 43\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4.10 Summary of Discrete Distributions 44\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5 Random Variables 45\u003c\/p\u003e \u003cp\u003e5.1 Definition of Random Variables 45\u003c\/p\u003e \u003cp\u003e5.2 Determination of Distribution and Density Functions 46\u003c\/p\u003e \u003cp\u003e5.3 Properties of Distribution and Density Functions 50\u003c\/p\u003e \u003cp\u003e5.4 Distribution Functions from Density Functions 51\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Continuous Random Variables and Basic Distributions 54\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 54\u003c\/p\u003e \u003cp\u003e6.2 Uniform Distribution 54\u003c\/p\u003e \u003cp\u003e6.3 Exponential Distribution 55\u003c\/p\u003e \u003cp\u003e6.4 Normal or Gaussian Distribution 57\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Other Continuous Distributions 63\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 63\u003c\/p\u003e \u003cp\u003e7.2 Triangular Distribution 63\u003c\/p\u003e \u003cp\u003e7.3 Laplace Distribution 63\u003c\/p\u003e \u003cp\u003e7.4 Erlang Distribution 64\u003c\/p\u003e \u003cp\u003e7.5 Gamma Distribution 65\u003c\/p\u003e \u003cp\u003e7.6 Weibull Distribution 66\u003c\/p\u003e \u003cp\u003e7.7 Chi-Square Distribution 67\u003c\/p\u003e \u003cp\u003e7.8 Chi and Other Allied Distributions 68\u003c\/p\u003e \u003cp\u003e7.9 Student-t Density 71\u003c\/p\u003e \u003cp\u003e7.10 Snedecor F Distribution 72\u003c\/p\u003e \u003cp\u003e7.11 Lognormal Distribution 72\u003c\/p\u003e \u003cp\u003e7.12 Beta Distribution 73\u003c\/p\u003e \u003cp\u003e7.13 Cauchy Distribution 74\u003c\/p\u003e \u003cp\u003e7.14 Pareto Distribution 75\u003c\/p\u003e \u003cp\u003e7.15 Gibbs Distribution 75\u003c\/p\u003e \u003cp\u003e7.16 Mixed Distributions 75\u003c\/p\u003e \u003cp\u003e7.17 Summary of Distributions of Continuous Random Variables 76\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Conditional Densities and Distributions 78\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Conditional Distribution and Density for P{A} 0 78\u003c\/p\u003e \u003cp\u003e8.2 Conditional Distribution and Density for P{A} = 0 80\u003c\/p\u003e \u003cp\u003e8.3 Total Probability and Bayes’ Theorem for Densities 83\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Joint Densities and Distributions 85\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Joint Discrete Distribution Functions 85\u003c\/p\u003e \u003cp\u003e9.2 Joint Continuous Distribution Functions 86\u003c\/p\u003e \u003cp\u003e9.3 Bivariate Gaussian Distributions 90\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Moments and Conditional Moments 91\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Expectations 91\u003c\/p\u003e \u003cp\u003e10.2 Variance 92\u003c\/p\u003e \u003cp\u003e10.3 Means and Variances of Some Distributions 93\u003c\/p\u003e \u003cp\u003e10.4 Higher-Order Moments 94\u003c\/p\u003e \u003cp\u003e10.5 Correlation and Partial Correlation Coefficients 95\u003c\/p\u003e \u003cp\u003e10.5.1 Correlation Coefficients 95\u003c\/p\u003e \u003cp\u003e10.5.2 Partial Correlation Coefficients 106\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Characteristic Functions and Generating Functions 108\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Characteristic Functions 108\u003c\/p\u003e \u003cp\u003e11.2 Examples of Characteristic Functions 109\u003c\/p\u003e \u003cp\u003e11.3 Generating Functions 111\u003c\/p\u003e \u003cp\u003e11.4 Examples of Generating Functions 112\u003c\/p\u003e \u003cp\u003e11.5 Moment Generating Functions 113\u003c\/p\u003e \u003cp\u003e11.6 Cumulant Generating Functions 115\u003c\/p\u003e \u003cp\u003e11.7 Table of Means and Variances 116\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Functions of a Single Random Variable 118\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Random Variable g(X) 118\u003c\/p\u003e \u003cp\u003e12.2 Distribution of Y = g(X) 119\u003c\/p\u003e \u003cp\u003e12.3 Direct Determination of Density fY(y) from fX(x) 129\u003c\/p\u003e \u003cp\u003e12.4 Inverse Problem: Finding g(X) given fX(x) and fY(y) 132\u003c\/p\u003e \u003cp\u003e12.5 Moments of a Function of a Random Variable 133\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Functions of Multiple Random Variables 135\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Function of Two Random Variables, Z = g(X,Y) 135\u003c\/p\u003e \u003cp\u003e13.2 Two Functions of Two Random Variables, Z = g(X,Y), W= h(X,Y) 143\u003c\/p\u003e \u003cp\u003e13.3 Direct Determination of Joint Density fZW(z,w) from fXY(x,y) 146\u003c\/p\u003e \u003cp\u003e13.4 Solving Z = g(X,Y) Using an Auxiliary Random Variable 150\u003c\/p\u003e \u003cp\u003e13.5 Multiple Functions of Random Variables 153\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Inequalities, Convergences, and Limit Theorems 155\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Degenerate Random Variables 155\u003c\/p\u003e \u003cp\u003e14.2 Chebyshev and Allied Inequalities 155\u003c\/p\u003e \u003cp\u003e14.3 Markov Inequality 158\u003c\/p\u003e \u003cp\u003e14.4 Chernoff Bound 159\u003c\/p\u003e \u003cp\u003e14.5 Cauchy–Schwartz Inequality 160\u003c\/p\u003e \u003cp\u003e14.6 Jensen’s Inequality 162\u003c\/p\u003e \u003cp\u003e14.7 Convergence Concepts 163\u003c\/p\u003e \u003cp\u003e14.8 Limit Theorems 165\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Computer Methods for Generating Random Variates 169\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Uniform-Distribution Random Variates 169\u003c\/p\u003e \u003cp\u003e15.2 Histograms 170\u003c\/p\u003e \u003cp\u003e15.3 Inverse Transformation Techniques 172\u003c\/p\u003e \u003cp\u003e15.4 Convolution Techniques 178\u003c\/p\u003e \u003cp\u003e15.5 Acceptance–Rejection Techniques 178\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Elements of Matrix Algebra 181\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Basic Theory of Matrices 181\u003c\/p\u003e \u003cp\u003e16.2 Eigenvalues and Eigenvectors of Matrices 186\u003c\/p\u003e \u003cp\u003e16.3 Vector and Matrix Differentiation 190\u003c\/p\u003e \u003cp\u003e16.4 Block Matrices 194\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Random Vectors and Mean-Square Estimation 196\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Distributions and Densities 196\u003c\/p\u003e \u003cp\u003e17.2 Moments of Random Vectors 200\u003c\/p\u003e \u003cp\u003e17.3 Vector Gaussian Random Variables 204\u003c\/p\u003e \u003cp\u003e17.4 Diagonalization of Covariance Matrices 207\u003c\/p\u003e \u003cp\u003e17.5 Simultaneous Diagonalization of Covariance Matrices 209\u003c\/p\u003e \u003cp\u003e17.6 Linear Estimation of Vector Variables 210\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Estimation Theory 212\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Criteria of Estimators 212\u003c\/p\u003e \u003cp\u003e18.2 Estimation of Random Variables 213\u003c\/p\u003e \u003cp\u003e18.3 Estimation of Parameters (Point Estimation) 218\u003c\/p\u003e \u003cp\u003e18.4 Interval Estimation (Confidence Intervals) 225\u003c\/p\u003e \u003cp\u003e18.5 Hypothesis Testing (Binary) 231\u003c\/p\u003e \u003cp\u003e18.6 Bayesian Estimation 238\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Random Processes 250\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Basic Definitions 250\u003c\/p\u003e \u003cp\u003e19.2 Stationary Random Processes 258\u003c\/p\u003e \u003cp\u003e19.3 Ergodic Processes 269\u003c\/p\u003e \u003cp\u003e19.4 Estimation of Parameters of Random Processes 273\u003c\/p\u003e \u003cp\u003e19.4.1 Continuous-Time Processes 273\u003c\/p\u003e \u003cp\u003e19.4.2 Discrete-Time Processes 280\u003c\/p\u003e \u003cp\u003e19.5 Power Spectral Density 287\u003c\/p\u003e \u003cp\u003e19.5.1 Continuous Time 287\u003c\/p\u003e \u003cp\u003e19.5.2 Discrete Time 294\u003c\/p\u003e \u003cp\u003e19.6 Adaptive Estimation 298\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Classification of Random Processes 320\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 Specifications of Random Processes 320\u003c\/p\u003e \u003cp\u003e20.1.1 Discrete-State Discrete-Time (DSDT) Process 320\u003c\/p\u003e \u003cp\u003e20.1.2 Discrete-State Continuous-Time (DSCT) Process 320\u003c\/p\u003e \u003cp\u003e20.1.3 Continuous-State Discrete-Time (CSDT) Process 320\u003c\/p\u003e \u003cp\u003e20.1.4 Continuous-State Continuous-Time (CSCT) Process 320\u003c\/p\u003e \u003cp\u003e20.2 Poisson Process 321\u003c\/p\u003e \u003cp\u003e20.3 Binomial Process 329\u003c\/p\u003e \u003cp\u003e20.4 Independent Increment Process 330\u003c\/p\u003e \u003cp\u003e20.5 Random-Walk Process 333\u003c\/p\u003e \u003cp\u003e20.6 Gaussian Process 338\u003c\/p\u003e \u003cp\u003e20.7 Wiener Process (Brownian Motion) 340\u003c\/p\u003e \u003cp\u003e20.8 Markov Process 342\u003c\/p\u003e \u003cp\u003e20.9 Markov Chains 347\u003c\/p\u003e \u003cp\u003e20.10 Birth and Death Processes 357\u003c\/p\u003e \u003cp\u003e20.11 Renewal Processes and Generalizations 366\u003c\/p\u003e \u003cp\u003e20.12 Martingale Process 370\u003c\/p\u003e \u003cp\u003e20.13 Periodic Random Process 374\u003c\/p\u003e \u003cp\u003e20.14 Aperiodic Random Process (Karhunen–Loeve Expansion) 377\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Random Processes and Linear Systems 383\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21.1 Review of Linear Systems 383\u003c\/p\u003e \u003cp\u003e21.2 Random Processes through Linear Systems 385\u003c\/p\u003e \u003cp\u003e21.3 Linear Filters 393\u003c\/p\u003e \u003cp\u003e21.4 Bandpass Stationary Random Processes 401\u003c\/p\u003e \u003cp\u003e\u003cb\u003e22 Wiener and Kalman Filters 413\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e22.1 Review of Orthogonality Principle 413\u003c\/p\u003e \u003cp\u003e22.2 Wiener Filtering 414\u003c\/p\u003e \u003cp\u003e22.3 Discrete Kalman Filter 425\u003c\/p\u003e \u003cp\u003e22.4 Continuous Kalman Filter 433\u003c\/p\u003e \u003cp\u003e\u003cb\u003e23 Probability Modeling in Traffic Engineering 437\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e23.1 Introduction 437\u003c\/p\u003e \u003cp\u003e23.2 Teletraffic Models 437\u003c\/p\u003e \u003cp\u003e23.3 Blocking Systems 438\u003c\/p\u003e \u003cp\u003e23.4 State Probabilities for Systems with Delays 440\u003c\/p\u003e \u003cp\u003e23.5 Waiting-Time Distribution for M\/M\/c\/∞ Systems 441\u003c\/p\u003e \u003cp\u003e23.6 State Probabilities for M\/D\/c Systems 443\u003c\/p\u003e \u003cp\u003e23.7 Waiting-Time Distribution for M\/D\/c\/∞ System 446\u003c\/p\u003e \u003cp\u003e23.8 Comparison of M\/M\/c and M\/D\/c 448\u003c\/p\u003e \u003cp\u003eReferences 451\u003c\/p\u003e \u003cp\u003e\u003cb\u003e24 Probabilistic Methods in Transmission Tomography 452\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e24.1 Introduction 452\u003c\/p\u003e \u003cp\u003e24.2 Stochastic Model 453\u003c\/p\u003e \u003cp\u003e24.3 Stochastic Estimation Algorithm 455\u003c\/p\u003e \u003cp\u003e24.4 Prior Distribution P{M} 457\u003c\/p\u003e \u003cp\u003e24.5 Computer Simulation 458\u003c\/p\u003e \u003cp\u003e24.6 Results and Conclusions 460\u003c\/p\u003e \u003cp\u003e24.7 Discussion of Results 462\u003c\/p\u003e \u003cp\u003eReferences 462\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAPPENDICES\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA A Fourier Transform Tables 463\u003c\/p\u003e \u003cp\u003eB Cumulative Gaussian Tables 467\u003c\/p\u003e \u003cp\u003eC Inverse Cumulative Gaussian Tables 472\u003c\/p\u003e \u003cp\u003eD Inverse Chi-Square Tables 474\u003c\/p\u003e \u003cp\u003eE Inverse Student-t Tables 481\u003c\/p\u003e \u003cp\u003eF Cumulative Poisson Distribution 484\u003c\/p\u003e \u003cp\u003eG Cumulative Binomial Distribution 488\u003c\/p\u003e \u003cp\u003eH Computation of Roots of D(z) = 0 494\u003c\/p\u003e \u003cp\u003eReferences 495\u003c\/p\u003e \u003cp\u003eIndex 498\u003c\/p\u003e  \u003cb\u003eVenkatarama Krishnan, PhD.,\u003c\/b\u003e is Professor Emeritus in the Department of Electrical and Computer Engineering at the University of Massachusetts at Lowell. He has served as a consultant to the Dynamics Research Corporation, the U.S. Department of Transportation, and Bell Laboratories. Dr. Krishnan’s research includes estimation of steady-state queue distribution, tomographic imaging, aerospace, control, communications, and stochastic systems. Dr. Krishnan is a senior member of the IEEE and listed in Who is Who in America.  \u003cp\u003e\u003cb\u003eThe second edition enhanced with new chapters, figures, and appendices to cover the new developments in applied mathematical functions\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThis book examines the topics of applied mathematical functions to problems that engineers and researchers solve daily in the course of their work. The text covers set theory, combinatorics, random variables, discrete and continuous probability, distribution functions, convergence of random variables, computer generation of random variates, random processes and stationarity concepts with associated autocovariance and cross covariance functions, estimation theory and Wiener and Kalman filtering ending with two applications of probabilistic methods. Probability tables with nine decimal place accuracy and graphical Fourier transform tables are included for quick reference. The author facilitates understanding of probability concepts for both students and practitioners by presenting over 450 carefully detailed figures and illustrations, and over 350 examples with every step explained clearly and some with multiple solutions.\u003c\/p\u003e \u003cp\u003eAdditional features of the second edition of \u003ci\u003eProbability and Random Processes\u003c\/i\u003e are:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eUpdated chapters with new sections on Newton-Pepys’ problem; Pearson, Spearman, and Kendal correlation coefficients; adaptive estimation techniques; birth and death processes; and renewal processes with generalizations\u003c\/li\u003e \u003cli\u003eA new chapter on Probability Modeling in Teletraffic Engineering written by Kavitha Chandra\u003c\/li\u003e \u003cli\u003eAn eighth appendix examining the computation of the roots of discrete probability-generating functions\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eWith new material on theory and applications of probability, \u003ci\u003eProbability and Random Processes, Second Edition\u003c\/i\u003e is a thorough and comprehensive reference for commonly occurring problems in probabilistic methods and their applications.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eVenkatarama Krishnan, PhD.,\u003c\/b\u003e is Professor Emeritus in the Department of Electrical and Computer Engineering at the University of Massachusetts at Lowell. He has served as a consultant to the Dynamics Research Corporation, the U.S. Department of Transportation, and Bell Laboratories. Dr. Krishnan’s research includes estimation of steady-state queue distribution, tomographic imaging, aerospace, control, communications, and stochastic systems. Dr. Krishnan is a senior member of the IEEE and listed in Who is Who in America.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989857452261,"sku":"NP9781118923139","price":136.5,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118923139.jpg?v=1761785698","url":"https:\/\/k12savings.com\/es\/products\/probability-and-random-processes-isbn-9781118923139","provider":"K12savings","version":"1.0","type":"link"}