Fundamentals of Applied Probability and Random Processes - 1st Edition

Fundamentals of Applied Probability and Random Processes

1st Edition

Authors: Oliver Ibe Oliver Ibe
Imprint: Academic Press
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Description

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-study.

Key Features

  • Good and solid introduction to probability theory and stochastic processes
  • Logically organized; writing is presented in a clear manner
  • Choice of topics is comprehensive within the area of probability
  • Ample homework problems are organized into chapter sections

Readership

Juniors and Seniors, but can also be used at lower graduate levels. Particularily welcome at engineering schools.

Table of Contents

Preface
Acknowledgments
Chapter 1 Basic Probability Concepts
1.1 Introduction
1.2 Sample Space and Events
1.3 Definitions of Probability
1.3.1 Axiomatic Definition
1.3.2 Relative-Frequency Definition
1.3.3 Classical Definition
1.4 Applications of Probability
1.4.1 Reliability Engineering
1.4.2 Quality Control
1.4.3 Channel Noise
1.4.4 System Simulation
1.5 Elementary Set Theory
1.5.1 Set Operations
1.5.2 Number of Subsets of a Set
1.5.3 Venn Diagram
1.5.4 Set Identities
1.5.5 Duality Principle
1.6 Properties of Probability
1.7 Conditional Probability
1.7.1 Total Probability and the Bayes’ Theorem
1.7.2 Tree Diagram
1.8 Independent Events
1.9 Combined Experiments
1.10 Basic Combinatorial Analysis
1.10.1 Permutations
1.10.2 Circular Arrangement
1.10.3 Applications of Permutations in Probability
1.10.4 Combinations
1.10.5 The Binomial Theorem
1.10.6 Stirling’s Formula
1.10.7 Applications of Combinations in Probability
1.11 Reliability Applications
1.12 Summary
1.13 Problems
1.14 References
Chapter 2 Random Variables
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
2.5.1 Obtaining the PMF from the CDF
2.6 Continuous Random Variables
2.7

Details

Language:
English
Imprint:
Academic Press
eBook ISBN:
9780080492704

About the Author

Oliver Ibe

Dr Ibe has been teaching at U Mass since 2003. He also has more than 20 years of experience in the corporate world, most recently as Chief Technology Officer at Sineria Networks and Director of Network Architecture for Spike Broadband Corp.

Affiliations and Expertise

University of Massachusetts, Lowell, USA

Oliver Ibe

Dr Ibe has been teaching at U Mass since 2003. He also has more than 20 years of experience in the corporate world, most recently as Chief Technology Officer at Sineria Networks and Director of Network Architecture for Spike Broadband Corp.

Affiliations and Expertise

University of Massachusetts, Lowell, USA

Reviews

"Each chapter is broken down into small subunits, making this a useful reference book as well as a textbook. The material is presented clearly, and solved problems are included in the text." --MAA Reviews