LEADER 05292nam 2200625Ia 450 001 9910784551103321 005 20230617005245.0 010 $a1-281-00493-6 010 $a9786611004934 010 $a0-08-049270-3 035 $a(CKB)1000000000364693 035 $a(EBL)294603 035 $a(OCoLC)469590054 035 $a(SSID)ssj0000159827 035 $a(PQKBManifestationID)11151856 035 $a(PQKBTitleCode)TC0000159827 035 $a(PQKBWorkID)10179487 035 $a(PQKB)10614462 035 $a(MiAaPQ)EBC294603 035 $a(Au-PeEL)EBL294603 035 $a(CaPaEBR)ebr10185953 035 $a(CaONFJC)MIL100493 035 $a(EXLCZ)991000000000364693 100 $a20050630d2005 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFundamentals of applied probability and random processes$b[electronic resource] /$fOliver C. Ibe 210 $aBurlington, MA ;$aLondon $cElsevier Academic Press$dc2005 215 $a1 online resource (461 p.) 300 $aDescription based upon print version of record. 311 $a0-12-088508-5 320 $aIncludes bibliographical references (p. 429-431) and index. 327 $aFront Cover; Fundamentals of Applied Probability and Random Processes; Copyright Page; Table of Contents; Preface; Acknowledgment; Chapter 1. Basic Probability Concepts; 1.1 Introduction; 1.2 Sample Space and Events; 1.3 Definitions of Probability; 1.4 Applications of Probability; 1.5 Elementary Set Theory; 1.6 Properties of Probability; 1.7 Conditional Probability; 1.8 Independent Events; 1.9 Combined Experiments; 1.10 Basic Combinatorial Analysis; 1.11 Reliability Applications; 1.12 Chapter Summary; 1.13 Problems; 1.14 References; Chapter 2. Random Variables; 2.1 Introduction 327 $a2.2 Definition of a Random Variable2.3 Events Defined by Random Variables; 2.4 Distribution Functions; 2.5 Discrete Random Variables; 2.6 Continuous Random Variables; 2.7 Chapter Summary; 2.8 Problems; Chapter 3. Moments of Random Variables; 3.1 Introduction; 3.2 Expectation; 3.3 Expectation of Nonnegative Random Variables; 3.4 Moments of Random Variables and the Variance; 3.5 Conditional Expectations; 3.6 The Chebyshev Inequality; 3.7 The Markov Inequality; 3.8 Chapter Summary; 3.9 Problems; Chapter 4. Special Probability Distributions; 4.1 Introduction 327 $a4.2 The Bernoulli Trial and Bernoulli Distribution4.3 Binomial Distribution; 4.4 Geometric Distribution; 4.5 Pascal (or Negative Binomial) Distribution; 4.6 Hypergeometric Distribution; 4.7 Poisson Distribution; 4.8 Exponential Distribution; 4.9 Erlang Distribution; 4.10 Uniform Distribution; 4.11 Normal Distribution; 4.12 The Hazard Function; 4.13 Chapter Summary; 4.14 Problems; Chapter 5. Multiple Random Variables; 5.1 Introduction; 5.2 Joint CDFs of Bivariate Random Variables; 5.3 Discrete Random Variables; 5.4 Continuous Random Variables; 5.5 Determining Probabilities from a Joint CDF 327 $a5.6 Conditional Distributions5.7 Covariance and Correlation Coefficient; 5.8 Many Random Variables; 5.9 Multinomial Distributions; 5.10 Chapter Summary; 5.11 Problems; Chapter 6. Functions of Random Variables; 6.1 Introduction; 6.2 Functions of One Random Variable; 6.3 Expectation of a Function of One Random Variable; 6.4 Sums of Independent Random Variables; 6.5 Minimum of Two Independent Random Variables; 6.6 Maximum of Two Independent Random Variables; 6.7 Comparison of the Interconnection Models; 6.8 Two Functions of Two Random Variables; 6.9 Laws of Large Numbers 327 $a6.10 The Central Limit Theorem6.11 Order Statistics; 6.12 Chapter Summary; 6.13 Problems; Chapter 7. Transform Methods; 7.1 Introduction; 7.2 The Characteristic Function; 7.3 The s-Transform; 7.4 The z-Transform; 7.5 Random Sum of Random Variables; 7.6 Chapter Summary; 7.7 Problems; Chapter 8. Introduction to Random Processes; 8.1 Introduction; 8.2 Classification of Random Processes; 8.3 Characterizing a Random Process; 8.4 Crosscorrelation and Crosscovariance Functions; 8.5 Stationary Random Processes; 8.6 Ergodic Random Processes; 8.7 Power Spectral Density 327 $a8.8 Discrete-Time Random Processes 330 $aThis book is based on the premise that engineers use probability as a modeling tool, and that probability can be applied to the solution of engineering problems. Engineers and students studying probability and random processes also need to analyze data, and thus need some knowledge of statistics. This book is designed to provide students with a thorough grounding in probability and stochastic processes, demonstrate their applicability to real-world problems, and introduce the basics of statistics. The book's clear writing style and homework problems make it ideal for the classroom or for self- 606 $aProbabilities 606 $aStochastic processes 615 0$aProbabilities. 615 0$aStochastic processes. 676 $a519.2 700 $aIbe$b Oliver C$g(Oliver Chukwudi),$f1947-$0522175 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910784551103321 996 $aFundamentals of applied probability and random processes$92205617 997 $aUNINA