Fundamentals of applied probability and random processes [[electronic resource] /] / Oliver C. Ibe

• Record Nr.: UNINA9910458476603321
• Autore: Ibe Oliver C (Oliver Chukwudi), <1947->
• Pubbl/distr/stampa: Burlington, MA ; ; London, : Elsevier Academic Press, c2005
• ISBN: 1-281-00493-6; 9786611004934; 0-08-049270-3
• Descrizione fisica: 1 online resource (461 p.)
• Disciplina: 519.2
• Soggetti: Probabilities; Stochastic processes; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. 429-431) and index.
• Nota di contenuto: Front 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; 2.2 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; 4.2 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; 5.6 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; 6.10 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; 8.8 Discrete-Time Random Processes
• Sommario/riassunto: This 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-