Probability, random variables, statistics, and random processes : (Record no. 75056)
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| fixed length control field | 12855nam a2200565 i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 8689276 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20220712211828.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 190417s2019 mau ob 001 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9781119300847 |
| -- | electronic bk. |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| -- | |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| -- | electronic bk. |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| -- | electronic bk. |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| -- | electronic bk. |
| 082 04 - CLASSIFICATION NUMBER | |
| Call Number | 519.2 |
| 100 1# - AUTHOR NAME | |
| Author | Grami, Ali, |
| 245 10 - TITLE STATEMENT | |
| Title | Probability, random variables, statistics, and random processes : |
| Sub Title | fundamentals & applications / |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | 1 PDF (416 pages). |
| 500 ## - GENERAL NOTE | |
| Remark 1 | Includes index. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Remark 2 | Preface 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# - FORMATTED CONTENTS NOTE | |
| Remark 2 | 4.7.1 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# - FORMATTED CONTENTS NOTE | |
| Remark 2 | 6.5 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# - FORMATTED CONTENTS NOTE | |
| Remark 2 | 8.5 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# - FORMATTED CONTENTS NOTE | |
| Remark 2 | 11.5.2 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. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | Probability, 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. |
| 856 42 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://ieeexplore.ieee.org/xpl/bkabstractplus.jsp?bkn=8689276 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks |
| 264 #1 - | |
| -- | Hoboken, New Jersey : |
| -- | Wiley, |
| -- | 2020. |
| 264 #2 - | |
| -- | [Piscataqay, New Jersey] : |
| -- | IEEE Xplore, |
| -- | [2019] |
| 336 ## - | |
| -- | text |
| -- | rdacontent |
| 337 ## - | |
| -- | electronic |
| -- | isbdmedia |
| 338 ## - | |
| -- | online resource |
| -- | rdacarrier |
| 588 0# - | |
| -- | Online resource; title from PDF title page (EBSCO, viewed March 11, 2019) |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Probabilities |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Statistics |
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