Fundamentals of Applied Probability and Random Processes

Oliver Ibe

• Publisher: Academic Press
• Year: 2014
• eBook ISBN: 9780128010358
• Edition: 2
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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 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).

Chapter 1

Basic Probability Concepts

Abstract

This chapter deals with basic concepts in probability including sample space and events, elementary set theory, conditional probability, independent events, basic combinatorial analysis, and applications of probability.

Keywords

Sample space

probability

conditional probability

reliability function

1.1 Introduction

Probability deals with unpredictability and randomness, and probability theory is the branch of mathematics that is concerned with the study of random phenomena. A random phenomenon is one that, under repeated observation, yields different outcomes that are not deterministically predictable. However, these outcomes obey certain conditions of statistical regularity whereby the relative frequency of occurrence of the possible outcomes is approximately predictable. Examples of these random phenomena include the number of electronic mail (e-mail) messages received by all employees of a company in one day, the number of phone calls arriving at the university’s switchboard over a given period, the number of components of a system that fail within a given interval, and the number of A’s that a student can receive in one academic year.

According to the preceding definition, the fundamental issue in random phenomena is the idea of a repeated experiment with a set of possible outcomes or events. Associated with each of these events is a real number called the probability of the event that is related to the frequency of occurrence of the event in a long sequence of repeated trials of the experiment. In this way it becomes obvious that the probability of an ...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Acknowledgment
• Preface to the Second Edition
• Preface to First Edition
• Chapter 1: Basic Probability Concepts
• Chapter 2: Random Variables
• Chapter 3: Moments of Random Variables
• Chapter 4: Special Probability Distributions
• Chapter 5: Multiple Random Variables
• Chapter 6: Functions of Random Variables
• Chapter 7: Transform Methods
• Chapter 8: Introduction to Descriptive Statistics
• Chapter 9: Introduction to Inferential Statistics
• Chapter 10: Introduction to Random Processes
• Chapter 11: Linear Systems with Random Inputs
• Chapter 12: Special Random Processes
• Appendix: Table of CDF of the Standard Normal Random Variable
• Bibliography
• Index