000 12855nam a2200565 i 4500
001 8689276
003 IEEE
005 20220712211828.0
006 m o d
007 cr |n|||||||||
008 190417s2019 mau ob 001 eng d
020 _a9781119300847
_qelectronic bk.
020 _z9781119300816
_qprint
020 _z1119300843
_qelectronic bk.
020 _z9781119300823
_qelectronic bk.
020 _z1119300827
_qelectronic bk.
024 7 _a10.1002/9781119300847
_2doi
035 _a(CaBNVSL)mat08689276
035 _a(IDAMS)0b0000648908bf78
040 _aCaBNVSL
_beng
_erda
_cCaBNVSL
_dCaBNVSL
050 4 _aQA273
082 0 4 _a519.2
_223
100 1 _aGrami, Ali,
_d1955-
_eauthor.
_931408
245 1 0 _aProbability, random variables, statistics, and random processes :
_bfundamentals & applications /
_cAli Grami.
264 1 _aHoboken, New Jersey :
_bWiley,
_c2020.
264 2 _a[Piscataqay, New Jersey] :
_bIEEE Xplore,
_c[2019]
300 _a1 PDF (416 pages).
336 _atext
_2rdacontent
337 _aelectronic
_2isbdmedia
338 _aonline resource
_2rdacarrier
500 _aIncludes index.
505 0 _aPreface xiii -- Acknowledgments xv -- About the Companion Website xvii -- Part I Probability 1 -- 1 Basic Concepts of Probability Theory 3 -- 1.1 Statistical Regularity and Relative Frequency 3 -- 1.2 Set Theory and Its Applications to Probability 5 -- 1.3 The Axioms and Corollaries of Probability 12 -- 1.4 Joint Probability and Conditional Probability 18 -- 1.5 Statistically Independent Events and Mutually Exclusive Events 21 -- 1.6 Law of Total Probability and Bayes’ Theorem 28 -- 1.7 Summary 32 -- Problems 32 -- 2 Applications in Probability 37 -- 2.1 Odds and Risk 37 -- 2.2 Gambler’s Ruin Problem 41 -- 2.3 Systems Reliability 43 -- 2.4 Medical Diagnostic Testing 47 -- 2.5 Bayesian Spam Filtering 50 -- 2.6 Monty Hall Problem 51 -- 2.7 Digital Transmission Error 54 -- 2.8 How to Make the Best Choice Problem 56 -- 2.9 The Viterbi Algorithm 59 -- 2.10 All Eggs in One Basket 61 -- 2.11 Summary 63 -- Problems 63 -- 3 Counting Methods and Applications 67 -- 3.1 Basic Rules of Counting 67 -- 3.2 Permutations and Combinations 72 -- 3.2.1 Permutations without Replacement 73 -- 3.2.2 Combinations without Replacement 73 -- 3.2.3 Permutations with Replacement 74 -- 3.2.4 Combinations with Replacement 74 -- 3.3 Multinomial Counting 77 -- 3.4 Special Arrangements and Selections 79 -- 3.5 Applications 81 -- 3.5.1 Game of Poker 81 -- 3.5.2 Birthday Paradox 83 -- 3.5.3 Quality Control 86 -- 3.5.4 Best-of-Seven Championship Series 86 -- 3.5.5 Lottery 89 -- 3.6 Summary 90 -- Problems 90 -- Part II Random Variables 95 -- 4 One Random Variable: Fundamentals 97 -- 4.1 Types of Random Variables 97 -- 4.2 The Cumulative Distribution Function 99 -- 4.3 The Probability Mass Function 102 -- 4.4 The Probability Density Function 104 -- 4.5 Expected Values 107 -- 4.5.1 Mean of a Random Variable 107 -- 4.5.2 Variance of a Random Variable 110 -- 4.5.3 Moments of a Random Variable 113 -- 4.5.4 Mode and Median of a Random Variable 114 -- 4.6 Conditional Distributions 116 -- 4.7 Functions of a Random Variable 120.
505 8 _a4.7.1 pdf of a Function of a Continuous Random Variable 121 -- 4.7.2 pmf of a Function of a Discrete Random Variable 123 -- 4.7.3 Computer Generation of Random Variables 124 -- 4.8 Transform Methods 125 -- 4.8.1 Moment Generating Function of a Random Variable 125 -- 4.8.2 Characteristic Function of a Random Variable 126 -- 4.9 Upper Bounds on Probability 127 -- 4.9.1 Markov Bound 127 -- 4.9.2 Chebyshev Bound 128 -- 4.9.3 Chernoff Bound 128 -- 4.10 Summary 131 -- Problems 131 -- 5 Special Probability Distributions and Applications 137 -- 5.1 Special Discrete Random Variables 137 -- 5.1.1 The Bernoulli Distribution 137 -- 5.1.2 The Binomial Distribution 138 -- 5.1.3 The Geometric Distribution 140 -- 5.1.4 The Pascal Distribution 142 -- 5.1.5 The Hypergeometric Distribution 143 -- 5.1.6 The Poisson Distribution 144 -- 5.1.7 The Discrete Uniform Distribution 146 -- 5.1.8 The Zipf (Zeta) Distribution 147 -- 5.2 Special Continuous Random Variables 148 -- 5.2.1 The Continuous Uniform Distribution 148 -- 5.2.2 The Exponential Distribution 149 -- 5.2.3 The Gamma Distribution 151 -- 5.2.4 The Erlang Distribution 152 -- 5.2.5 The Weibull Distribution 152 -- 5.2.6 The Beta Distribution 153 -- 5.2.7 The Laplace Distribution 154 -- 5.2.8 The Pareto Distribution 155 -- 5.3 Applications 156 -- 5.3.1 Digital Transmission: Regenerative Repeaters 156 -- 5.3.2 System Reliability: Failure Rate 157 -- 5.3.3 Queuing Theory: Servicing Customers 158 -- 5.3.4 Random Access: Slotted ALOHA 159 -- 5.3.5 Analog-to-Digital Conversion: Quantization 160 -- 5.4 Summary 161 -- Problems 162 -- 6 Multiple Random Variables 165 -- 6.1 Pairs of Random Variables 165 -- 6.2 The Joint Cumulative Distribution Function of Two Random Variables 167 -- 6.2.1 Marginal Cumulative Distribution Function 169 -- 6.3 The Joint Probability Mass Function of Two Random Variables 170 -- 6.3.1 Marginal Probability Mass Function 170 -- 6.4 The Joint Probability Density Function of Two Random Variables 171 -- 6.4.1 Marginal Probability Density Function 172.
505 8 _a6.5 Expected Values of Functions of Two Random Variables 173 -- 6.5.1 Joint Moments 174 -- 6.6 Independence of Two Random Variables 175 -- 6.7 Correlation between Two Random Variables 178 -- 6.8 Conditional Distributions 185 -- 6.8.1 Conditional Expectations 186 -- 6.9 Distributions of Functions of Two Random Variables 188 -- 6.9.1 Joint Distribution of Two Functions of Two Random Variables 191 -- 6.10 Random Vectors 192 -- 6.11 Summary 197 -- Problems 198 -- 7 The Gaussian Distribution 201 -- 7.1 The Gaussian Random Variable 201 -- 7.2 The Standard Gaussian Distribution 204 -- 7.3 Bivariate Gaussian Random Variables 210 -- 7.3.1 Linear Transformations of Bivariate Gaussian Random Variables 213 -- 7.4 Jointly Gaussian Random Vectors 215 -- 7.5 Sums of Random Variables 217 -- 7.5.1 Mean and Variance of Sum of Random Variables 217 -- 7.5.2 Mean and Variance of Sum of Independent, Identically Distributed Random Variables 218 -- 7.5.3 Distribution of Sum of Independent Random Variables 218 -- 7.5.4 Sum of a Random Number of Independent, Identically Distributed Random Variables 219 -- 7.6 The Sample Mean 220 -- 7.6.1 Laws of Large Numbers 222 -- 7.7 Approximating Distributions with the Gaussian Distribution 223 -- 7.7.1 Relation between the Gaussian and Binomial Distributions 223 -- 7.7.2 Relation between the Gaussian and Poisson Distributions 225 -- 7.7.3 The Central Limit Theorem 226 -- 7.8 Probability Distributions Related to the Gaussian Distribution 230 -- 7.8.1 The Rayleigh Distribution 230 -- 7.8.2 The Ricean Distribution 231 -- 7.8.3 The Log-Normal Distribution 231 -- 7.8.4 The Chi-Square Distribution 232 -- 7.8.5 The Maxwell-Boltzmann Distribution 232 -- 7.8.6 The Student’s t-Distribution 233 -- 7.8.7 The F Distribution 234 -- 7.8.8 The Cauchy Distribution 234 -- 7.9 Summary 234 -- Problems 235 -- Part III Statistics 239 -- 8 Descriptive Statistics 241 -- 8.1 Overview of Statistics 241 -- 8.2 Data Displays 244 -- 8.3 Measures of Location 249 -- 8.4 Measures of Dispersion 250.
505 8 _a8.5 Measures of Shape 255 -- 8.6 Summary 257 -- Problems 257 -- 9 Estimation 259 -- 9.1 Parameter Estimation 259 -- 9.2 Properties of Point Estimators 260 -- 9.3 Maximum Likelihood Estimators 265 -- 9.4 Bayesian Estimators 270 -- 9.5 Confidence Intervals 272 -- 9.6 Estimation of a Random Variable 274 -- 9.7 Maximum a Posteriori Probability Estimation 275 -- 9.8 Minimum Mean Square Error Estimation 277 -- 9.9 Linear Minimum Mean Square Error Estimation 279 -- 9.10 Linear MMSE Estimation Using a Vector of Observations 282 -- 9.11 Summary 285 -- Problems 285 -- 10 Hypothesis Testing 287 -- 10.1 Significance Testing 287 -- 10.2 Hypothesis Testing for Mean 291 -- 10.2.1 p-Value 294 -- 10.3 Decision Tests 300 -- 10.4 Bayesian Test 303 -- 10.4.1 Minimum Cost Test 304 -- 10.4.2 Maximum a Posteriori Probability (MAP) Test 305 -- 10.4.3 Maximum-Likelihood (ML) Test 305 -- 10.4.4 Minimax Test 307 -- 10.5 Neyman-Pearson Test 307 -- 10.6 Summary 309 -- Problems 309 -- Part IV Random Processes 311 -- 11 Introduction to Random Processes 313 -- 11.1 Classification of Random Processes 313 -- 11.1.1 State Space 314 -- 11.1.2 Index (Time) Parameter 314 -- 11.2 Characterization of Random Processes 318 -- 11.2.1 Joint Distributions of Time Samples 318 -- 11.2.2 Independent Identically Distributed Random Process 319 -- 11.2.3 Multiple Random Processes 320 -- 11.2.4 Independent Random Processes 320 -- 11.3 Moments of Random Processes 320 -- 11.3.1 Mean and Variance Functions of a Random Process 321 -- 11.3.2 Autocorrelation and Autocovariance Functions of a Random Process 321 -- 11.3.3 Cross-correlation and Cross-covariance Functions 324 -- 11.4 Stationary Random Processes 326 -- 11.4.1 Strict-Sense Stationary Processes 326 -- 11.4.2 Wide-Sense Stationary Processes 327 -- 11.4.3 Jointly Wide-Sense Stationary Processes 329 -- 11.4.4 Cyclostationary Processes 331 -- 11.4.5 Independent and Stationary Increments 331 -- 11.5 Ergodic Random Processes 333 -- 11.5.1 Strict-Sense Ergodic Processes 333.
505 8 _a11.5.2 Wide-Sense Ergodic Processes 333 -- 11.6 Gaussian Processes 336 -- 11.7 Poisson Processes 339 -- 11.8 Summary 341 -- Problems 341 -- 12 Analysis and Processing of Random Processes 345 -- 12.1 Stochastic Continuity, Differentiation, and Integration 345 -- 12.1.1 Mean-Square Continuity 345 -- 12.1.2 Mean-Square Derivatives 346 -- 12.1.3 Mean-Square Integrals 347 -- 12.2 Power Spectral Density 347 -- 12.3 Noise 353 -- 12.3.1 White Noise 353 -- 12.4 Sampling of Random Signals 355 -- 12.5 Optimum Linear Systems 357 -- 12.5.1 Systems Maximizing Signal-to-Noise Ratio 357 -- 12.5.2 Systems Minimizing Mean-Square Error 359 -- 12.6 Summary 362 -- Problems 362 -- Bibliography 365 -- Books 365 -- Internet Websites 368 -- Answers 369 -- Index 387.
506 _aRestricted to subscribers or individual electronic text purchasers.
520 _aProbability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications is a comprehensive undergraduate-level textbook. With its excellent topical coverage, the focus of this book is on the basic principles and practical applications of the fundamental concepts that are extensively used in various Engineering disciplines as well as in a variety of programs in Life and Social Sciences. The text provides students with the requisite building blocks of knowledge they require to understand and progress in their areas of interest. With a simple, clear-cut style of writing, the intuitive explanations, insightful examples, and practical applications are the hallmarks of this book. The text consists of twelve chapters divided into four parts. Part-I, Probability "Chapters 1 – 3", lays a solid groundwork for probability theory, and introduces applications in counting, gambling, reliability, and security. Part-II, Random Variables "Chapters 4 – 7", discusses in detail multiple random variables, along with a multitude of frequently-encountered probability distributions. Part-III, Statistics "Chapters 8 – 10", highlights estimation and hypothesis testing. Part-IV, Random Processes "Chapters 11 – 12", delves into the characterization and processing of random processes. Other notable features are as follows: . Most of the text assumes no knowledge of subject matter past first year calculus and linear algebra. With its independent chapter structure and rich choice of topics, a variety of syllabi for different courses at the junior, senior, and graduate levels can be supported. A supplemental website includes solutions to about 250 practice problems, lecture slides, and figures and tables from the text Given its engaging tone, grounded approach, methodically-paced flow, thorough coverage, and flexible structure, Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications serves as an essential textbook for courses not only in Electrical Engineering, but also in Computer Engineering, Software Engineering, and Computer Science.
530 _aAlso available in print.
538 _aMode of access: World Wide Web
588 0 _aOnline resource; title from PDF title page (EBSCO, viewed March 11, 2019)
650 0 _aProbabilities
_vTextbooks.
_94442
650 0 _aStatistics
_vTextbooks.
_931409
655 4 _aElectronic books.
_93294
710 2 _aIEEE Xplore (Online Service),
_edistributor.
_931410
710 2 _aWiley,
_epublisher.
_931411
776 0 8 _iPrint version:
_z9781119300816
856 4 2 _3Abstract with links to resource
_uhttps://ieeexplore.ieee.org/xpl/bkabstractplus.jsp?bkn=8689276
942 _cEBK
999 _c75056
_d75056