LEADER 05368nam 22006614a 450 001 9910784646003321 005 20230120004753.0 010 $a1-280-96126-0 010 $a9786610961269 010 $a0-08-047042-4 035 $a(CKB)1000000000364543 035 $a(EBL)286732 035 $a(OCoLC)469400001 035 $a(SSID)ssj0000227861 035 $a(PQKBManifestationID)11174893 035 $a(PQKBTitleCode)TC0000227861 035 $a(PQKBWorkID)10270047 035 $a(PQKB)10190276 035 $a(MiAaPQ)EBC286732 035 $a(Au-PeEL)EBL286732 035 $a(CaPaEBR)ebr10167040 035 $a(CaONFJC)MIL96126 035 $a(EXLCZ)991000000000364543 100 $a20040430d2004 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aProbability and random processes$b[electronic resource] $ewith applications to signal processing and communications /$fScott L. Miller, Donald Childers 210 $aAmsterdam ;$aBoston $cElsevier Academic Press$dc2004 215 $a1 online resource (551 p.) 300 $aIncludes index. 311 $a1-4933-0026-1 311 $a0-12-172651-7 327 $aFront Cover; Probability and Random Processes; Copyright Page; Contents; Preface; Chapter 1. Introduction; 1.1 A Speech Recognition System; 1.2 A Radar System; 1.3 A Communication Network; Chapter 2. Introduction to Probability Theory; 2.1 Experiments, Sample Spaces, and Events; 2.2 Axioms of Probability; 2.3 Assigning Probabilities; 2.4 Joint and Conditional Probabilities; 2.5 Bayes's Theorem; 2.6 Independence; 2.7 Discrete Random Variables; 2.8 Engineering Application: An Optical Communication System; Chapter 3. Random Variables, Distributions, and Density Functions 327 $a3.1 The Cumulative Distribution Function3.2 The Probability Density Function; 3.3 The Gaussian Random Variable; 3.4 Other Important Random Variables; 3.5 Conditional Distribution and Density Functions; 3.6 Engineering Application: Reliability and Failure Rates; Chapter 4. Operations on a Single Random Variable; 4.1 Expected Value of a Random Variable; 4.2 Expected Values of Functions of Random Variables; 4.3 Moments; 4.4 Central Moments; 4.5 Conditional Expected Values; 4.6 Transformations of Random Variables; 4.7 Characteristic Functions; 4.8 Probability Generating Functions 327 $a4.9 Moment Generating Functions4.10 Evaluating Tail Probabilities; 4.11 Engineering Application: Scalar Quantization; 4.12 Engineering Application: Entropy and Source Coding; Chapter 5. Pairs of Random Variables; 5.1 Joint Cumulative Distribution Functions; 5.2 Joint Probability Density Functions; 5.3 Joint Probability Mass Functions; 5.4 Conditional Distribution, Density, and Mass Functions; 5.5 Expected Values Involving Pairs of Random Variables; 5.6 Independent Random Variables; 5.7 Jointly Gaussian Random Variables; 5.8 Joint Characteristic and Related Functions 327 $a5.9 Transformations of Pairs of Random Variables5.10 Complex Random Variables; 5.11 Engineering Application: Mutual Information, Channel Capacity, and Channel Coding; Chapter 6. Multiple Random Variables; 6.1 Joint and Conditional PMFs, CDFs, and PDFs; 6.2 Expectations Involving Multiple Random Variables; 6.3 Gaussian Random Variables in Multiple Dimensions; 6.4 Transformations Involving Multiple Random Variables; 6.5 Engineering Application: Linear Prediction of Speech; Chapter 7. Random Sequences and Series; 7.1 Independent and Identically Distributed Random Variables 327 $a7.2 Convergence Modes of Random Sequences7.3 The Law of Large Numbers; 7.4 The Central Limit Theorem; 7.5 Confidence Intervals; 7.6 Random Sums of Random Variables; 7.7 Engineering Application: A Radar System; Chapter 8. Random Processes; 8.1 Definition and Classification of Processes; 8.2 Mathematical Tools for Studying Random Processes; 8.3 Stationary and Ergodic Random Processes; 8.4 Properties of the Autocorrelation Function; 8.5 Gaussian Random Processes; 8.6 Poisson Processes; 8.7 Engineering Application: Shot Noise in a p-n Junction Diode; Chapter 9. Markov Processes 327 $a9.1 Definition and Examples of Markov Processes 330 $aMiller and Childers have focused on creating a clear presentation of foundational concepts with specific applications to signal processing and communications, clearly the two areas of most interest to students and instructors in this course. It is aimed at graduate students as well as practicing engineers, and includes unique chapters on narrowband random processes and simulation techniques. The appendices provide a refresher in such areas as linear algebra, set theory, random variables, and more. Probability and Random Processes also includes applications in digital communicat 606 $aSignal processing$xMathematics 606 $aProbabilities 606 $aStochastic processes 615 0$aSignal processing$xMathematics. 615 0$aProbabilities. 615 0$aStochastic processes. 676 $a621.382/2/0151 700 $aMiller$b Scott L$0223807 701 $aChilders$b Donald G$01549987 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910784646003321 996 $aProbability and random processes$93808439 997 $aUNINA