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# Fundamentals of Applied Probability and Random Processes

- 2nd Edition - June 13, 2014
- Author: Oliver Ibe
- Language: English
- Hardback ISBN:9 7 8 - 0 - 1 2 - 8 0 0 8 5 2 - 2
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 0 1 0 3 5 - 8

The long-awaited revision of Fundamentals of Applied Probability and Random Processes expands on the central components that made the first edition a classic. The title is based… Read more

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Request a sales quoteThe long-awaited revision of *Fundamentals of Applied Probability and Random Processes* expands on the central components that made the first edition a classic. The title 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-study.

- Demonstrates concepts with more than 100 illustrations, including 2 dozen new drawings
- Expands readers’ understanding of disruptive statistics in a new chapter (chapter 8)
- Provides new chapter on Introduction to Random Processes with 14 new illustrations and tables explaining key concepts.
- Includes two chapters devoted to the two branches of statistics, namely descriptive statistics (chapter 8) and inferential (or inductive) statistics (chapter 9).

- Acknowledgment
- Preface to the Second Edition
- Preface to First Edition
- Chapter 1: Basic Probability Concepts
- Abstract
- 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

- Chapter 2: Random Variables
- Abstract
- 2.1 Introduction
- 2.2 Definition of a Random Variable
- 2.3 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
- Abstract
- 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 Markov Inequality
- 3.7 The Chebyshev Inequality
- 3.8 Chapter Summary
- 3.9 Problems

- Chapter 4: Special Probability Distributions
- Abstract
- 4.1 Introduction
- 4.2 The Bernoulli Trial and Bernoulli Distribution
- 4.3 Binomial Distribution
- 4.4 Geometric Distribution
- 4.5 Pascal 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 Truncated Probability Distributions
- 4.14 Chapter Summary
- 4.15 Problems

- Chapter 5: Multiple Random Variables
- Abstract
- 5.1 Introduction
- 5.2 Joint CDFs of Bivariate Random Variables
- 5.3 Discrete Bivariate Random Variables
- 5.4 Continuous Bivariate Random Variables
- 5.5 Determining Probabilities from a Joint CDF
- 5.6 Conditional Distributions
- 5.7 Covariance and Correlation Coefficient
- 5.8 Multivariate Random Variables
- 5.9 Multinomial Distributions
- 5.10 Chapter Summary
- 5.11 Problems

- Chapter 6: Functions of Random Variables
- Abstract
- 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 Theorem
- 6.11 Order Statistics
- 6.12 Chapter Summary
- 6.13 Problems

- Chapter 7: Transform Methods
- Abstract
- 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 Descriptive Statistics
- Abstract
- 8.1 Introduction
- 8.2 Descriptive Statistics
- 8.3 Measures of Central Tendency
- 8.4 Measures of Dispersion
- 8.5 Graphical and Tabular Displays
- 8.6 Shape of Frequency Distributions: Skewness
- 8.7 Shape of Frequency Distributions: Peakedness
- 8.8 Chapter Summary
- 8.9 Problems

- Chapter 9: Introduction to Inferential Statistics
- Abstract
- 9.1 Introduction
- 9.2 Sampling Theory
- 9.3 Estimation Theory
- 9.4 Hypothesis Testing
- 9.5 Regression Analysis
- 9.6 Chapter Summary
- 9.7 Problems

- Chapter 10: Introduction to Random Processes
- Abstract
- 10.1 Introduction
- 10.2 Classification of Random Processes
- 10.3 Characterizing a Random Process
- 10.4 Crosscorrelation and Crosscovariance Functions
- 10.5 Stationary Random Processes
- 10.6 Ergodic Random Processes
- 10.7 Power Spectral Density
- 10.8 Discrete-Time Random Processes
- 10.9 Chapter Summary
- 10.10 Problems

- Chapter 11: Linear Systems with Random Inputs
- Abstract
- 11.1 Introduction
- 11.2 Overview of Linear Systems with Deterministic Inputs
- 11.3 Linear Systems with Continuous-time Random Inputs
- 11.4 Linear Systems with Discrete-time Random Inputs
- 11.5 Autoregressive Moving Average Process
- 11.6 Chapter Summary
- 11.7 Problems

- Chapter 12: Special Random Processes
- Abstract
- 12.1 Introduction
- 12.2 The Bernoulli Process
- 12.3 Random Walk Process
- 12.4 The Gaussian Process
- 12.5 Poisson Process
- 12.6 Markov Processes
- 12.7 Discrete-Time Markov Chains
- 12.8 Continuous-Time Markov Chains
- 12.9 Gambler’s Ruin as a Markov Chain
- 12.10 Chapter Summary
- 12.11 Problems

- Appendix: Table of CDF of the Standard Normal Random Variable
- Bibliography
- Index

- No. of pages: 456
- Language: English
- Edition: 2
- Published: June 13, 2014
- Imprint: Academic Press
- Hardback ISBN: 9780128008522
- eBook ISBN: 9780128010358

OI

### Oliver Ibe

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