Probability and random processes. (2015)

• Record Type: Book
• Further Information: Note: Venkatarama Krishnan and Kavitha Chandra.
• Authors: Krishnan, Venkatarama, 1929-
• Other Names: Chandra, Kavitha contributor.
• Contents: Preface for the Second Edition xii Preface for the First Edition xiv 1 Sets, Fields, and Events 1 1.1 Set Definitions, 1 1.2 Set Operations, 2 1.3 Set Algebras, Fields, and Events, 5 2 Probability Space and Axioms 7 2.1 Probability Space, 7 2.2 Conditional Probability, 9 2.3 Independence, 11 2.4 Total Probability and Bayes’ Theorem, 12 3 Basic Combinatorics 16 3.1 Basic Counting Principles, 16 3.2 Permutations, 16 3.3 Combinations, 18 4 Discrete Distributions 23 4.1 Bernoulli Trials, 23 4.2 Binomial Distribution, 23 4.3 Multinomial Distribution, 26 4.4 Geometric Distribution, 26 4.5 Negative Binomial Distribution, 27 4.6 Hypergeometric Distribution, 28 4.7 Poisson Distribution, 30 4.8 Newton–Pepys Problem and its Extensions, 33 4.9 Logarithmic Distribution, 40 4.9.1 Finite Law (Benford’s Law), 40 4.9.2 Infinite Law, 43 4.10 Summary of Discrete Distributions, 44 5 Random Variables 45 5.1 Definition of Random Variables, 45 5.2 Determination of Distribution and Density Functions, 46 5.3 Properties of Distribution and Density Functions, 50 5.4 Distribution Functions from Density Functions, 51 6 Continuous Random Variables and Basic Distributions 54 6.1 Introduction, 54 6.2 Uniform Distribution, 54 6.3 Exponential Distribution, 55 6.4 Normal or Gaussian Distribution, 57 7 Other Continuous Distributions 63 7.1 Introduction, 63 7.2 Triangular Distribution, 63 7.3 Laplace Distribution, 63 7.4 Erlang Distribution, 64 7.5 Gamma Distribution, 65 7.6 Weibull Distribution, 66 7.7 Chi-Square Distribution, 67 7.8 Chi and Other Allied Distributions, 68 7.9 Student-t Density, 71 7.10 Snedecor F Distribution, 72 7.11 Lognormal Distribution, 72 7.12 Beta Distribution, 73 7.13 Cauchy Distribution, 74 7.14 Pareto Distribution, 75 7.15 Gibbs Distribution, 75 7.16 Mixed Distributions, 75 7.17 Summary of Distributions of Continuous Random Variables, 76 8 Conditional Densities and Distributions 78 8.1 Conditional Distribution and Density for P{A} 0, 78 8.2 Conditional Distribution and Density for P{A} = 0, 80 8.3 Total Probability and Bayes’ Theorem for Densities, 83 9 Joint Densities and Distributions 85 9.1 Joint Discrete Distribution Functions, 85 9.2 Joint Continuous Distribution Functions, 86 9.3 Bivariate Gaussian Distributions, 90 10 Moments and Conditional Moments 91 10.1 Expectations, 91 10.2 Variance, 92 10.3 Means and Variances of Some Distributions, 93 10.4 Higher-Order Moments, 94 10.5 Correlation and Partial Correlation Coefficients, 95 10.5.1 Correlation Coefficients, 95 10.5.2 Partial Correlation Coefficients, 106 11 Characteristic Functions and Generating Functions 108 11.1 Characteristic Functions, 108 11.2 Examples of Characteristic Functions, 109 11.3 Generating Functions, 111 11.4 Examples of Generating Functions, 112 11.5 Moment Generating Functions, 113 11.6 Cumulant Generating Functions, 115 11.7 Table of Means and Variances, 116 12 Functions of a Single Random Variable 118 12.1 Random Variable g(X), 118 12.2 Distribution of Y = g(X), 119 12.3 Direct Determination of Density fY(y) from fX(x), 129 12.4 Inverse Problem: Finding g(X) given fX(x) and fY(y), 132 12.5 Moments of a Function of a Random Variable, 133 13 Functions of Multiple Random Variables 135 13.1 Function of Two Random Variables, Z = g(X, Y), 135 13.2 Two Functions of Two Random Variables, Z = g(X, Y), W= h(X, Y), 143 13.3 Direct Determination of Joint Density fZW(z, w) from fXY(x, y), 146 13.4 Solving Z = g(X, Y) Using an Auxiliary Random Variable, 150 13.5 Multiple Functions of Random Variables, 153 14 Inequalities, Convergences, and Limit Theorems 155 14.1 Degenerate Random Variables, 155 14.2 Chebyshev and Allied Inequalities, 155 14.3 Markov Inequality, 158 14.4 Chernoff Bound, 159 14.5 Cauchy–Schwartz Inequality, 160 14.6 Jensen’s Inequality, 162 14.7 Convergence Concepts, 163 14.8 Limit Theorems, 165 15 Computer Methods for Generating Random Variates 169 15.1 Uniform-Distribution Random Variates, 169 15.2 Histograms, 170 15.3 Inverse Transformation Techniques, 172 15.4 Convolution Techniques, 178 15.5 Acceptance–Rejection Techniques, 178 16 Elements of Matrix Algebra 181 16.1 Basic Theory of Matrices, 181 16.2 Eigenvalues and Eigenvectors of Matrices, 186 16.3 Vector and Matrix Differentiation, 190 16.4 Block Matrices, 194 17 Random Vectors and Mean-Square Estimation 196 17.1 Distributions and Densities, 196 17.2 Moments of Random Vectors, 200 17.3 Vector Gaussian Random Variables, 204 17.4 Diagonalization of Covariance Matrices, 207 17.5 Simultaneous Diagonalization of Covariance Matrices, 209 17.6 Linear Estimation of Vector Variables, 210 18 Estimation Theory 212 18.1 Criteria of Estimators, 212 18.2 Estimation of Random Variables, 213 18.3 Estimation of Parameters (Point Estimation), 218 18.4 Interval Estimation (Confidence Intervals), 225 18.5 Hypothesis Testing (Binary), 231 18.6 Bayesian Estimation, 238 19 Random Processes 250 19.1 Basic Definitions, 250 19.2 Stationary Random Processes, 258 19.3 Ergodic Processes, 269 19.4 Estimation of Parameters of Random Processes, 273 19.4.1 Continuous-Time Processes, 273 19.4.2 Discrete-Time Processes, 280 19.5 Power Spectral Density, 287 19.5.1 Continuous Time, 287 19.5.2 Discrete Time, 294 19.6 Adaptive Estimation, 298 20 Classification of Random Processes 320 20.1 Specifications of Random Processes, 320 20.1.1 Discrete-State Discrete-Time (DSDT) Process, 320 20.1.2 Discrete-State Continuous-Time (DSCT) Process, 320 20.1.3 Continuous-State Discrete-Time (CSDT) Process, 320 20.1.4 Continuous-State Continuous-Time (CSCT) Process, 320 20.2 Poisson Process, 321 20.3 Binomial Process, 329 20.4 Independent Increment Process, 330 20.5 Random-Walk Process, 333 20.6 Gaussian Process, 338 20.7 Wiener Process (Brownian Motion), 340 20.8 Markov Process, 342 20.9 Markov Chains, 347 20.10 Birth and Death Processes, 357 20.11 Renewal Processes and Generalizations, 366 20.12 Martingale Process, 370 20.13 Periodic Random Process, 374 20.14 Aperiodic Random Process (Karhunen–Loeve Expansion), 377 21 Random Processes and Linear Systems 383 21.1 Review of Linear Systems, 383 21.2 Random Processes through Linear Systems, 385 21.3 Linear Filters, 393 21.4 Bandpass Stationary Random Processes, 401 22 Wiener and Kalman Filters 413 22.1 Review of Orthogonality Principle, 413 22.2 Wiener Filtering, 414 22.3 Discrete Kalman Filter, 425 22.4 Continuous Ka
• Edition: Second edition
• Publisher Details: Hoboken : John Wiley & Sons
• Publication Date: 2015
• Extent: 1 online resource
• Subjects: 519.2; Probabilities; Stochastic processes; Engineering -- Statistical methods; Science -- Statistical methods
• Languages: English
• ISBNs: 9781119011903
• Related ISBNs: 9781119011910; 9781119011934
• Notes: Note: Description based on CIP data; resource not viewed.
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