Fundamentals of Applied Probability and Random Processes

ISBN-10: 0120885085

ISBN-13: 9780120885084

Edition: 2005

Authors: Oliver C. Ibe

List price: $133.00
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Offering a thorough introduction to probability theory and stochastic processes, this text features numerous illustrative examples that will enhance the learning experience of students.
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Book details

List price: $133.00
Copyright year: 2005
Publisher: Elsevier Science & Technology Books
Publication date: 10/19/2005
Binding: Hardcover
Pages: 456
Size: 7.75" wide x 9.25" long x 1.00" tall
Weight: 2.332
Language: English

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.

Preface
Acknowledgment
Basic Probability Concepts
Introduction
Sample Space and Events
Definitions of Probability
Axiomatic Definition
Relative-Frequency Definition
Classical Definition
Applications of Probability
Reliability Engineering
Quality Control
Channel Noise
System Simulation
Elementary Set Theory
Set Operations
Number of Subsets of a Set
Venn Diagram
Set Identities
Duality Principle
Properties of Probability
Conditional Probability
Total Probability and the Bayes' Theorem
Tree Diagram
Independent Events
Combined Experiments
Basic Combinatorial Analysis
Permutations
Circular Arrangement
Applications of Permutations in Probability
Combinations
The Binomial Theorem
Stirling's Formula
Applications of Combinations in Probability
Reliability Applications
Chapter Summary
Problems
References
Random Variables
Introduction
Definition of a Random Variable
Events Defined by Random Variables
Distribution Functions
Discrete Random Variables
Obtaining the PMF from the CDF
Continuous Random Variables
Chapter Summary
Problems
Moments of Random Variables
Introduction
Expectation
Expectation of Nonnegative Random Variables
Moments of Random Variables and the Variance
Conditional Expectations
The Chebyshev Inequality
The Markov Inequality
Chapter Summary
Problems
Special Probability Distributions
Introduction
The Bernoulli Trial and Bernoulli Distribution
Binomial Distribution
Geometric Distribution
Modified Geometric Distribution
"Forgetfulness" Property of the Geometric Distribution
Pascal (or Negative Binomial) Distribution
Hypergeometric Distribution
Poisson Distribution
Poisson Approximation to the Binomial Distribution
Exponential Distribution
"Forgetfulness" Property of the Exponential Distribution
Relationship between the Exponential and Poisson Distributions
Erlang Distribution
Uniform Distribution
The Discrete Uniform Distribution
Normal Distribution
Normal Approximation to the Binomial Distribution
The Error Function
The Q-Function
The Hazard Function
Chapter Summary
Problems
Multiple Random Variables
Introduction
Joint CDFs of Bivariate Random Variables
Properties of the Joint CDF
Discrete Random Variables
Continuous Random Variables
Determining Probabilities from a Joint CDF
Conditional Distributions
Conditional PMF for Discrete Random Variables
Conditional PDF for Continuous Random Variables
Conditional Means and Variances
Simple Rule for Independence
Covariance and Correlation Coefficient
Many Random Variables
Multinomial Distributions
Chapter Summary
Problems
Functions of Random Variables
Introduction
Functions of One Random Variable
Linear Functions
Power Functions
Expectation of a Function of One Random Variable
Moments of a Linear Function
Sums of Independent Random Variables
Moments of the Sum of Random Variables
Sum of Discrete Random Variables
Sum of Independent Binomial Random Variables
Sum of Independent Poisson Random Variables
The Spare Parts Problem
Minimum of Two Independent Random Variables
Maximum of Two Independent Random Variables
Comparison of the Interconnection Models
Two Functions of Two Random Variables
Application of the Transformation Method
Laws of Large Numbers
The Central Limit Theorem
Order Statistics
Chapter Summary
Problems
Transform Methods
Introduction
The Characteristic Function
Moment-Generating Property of the Characteristic Function
The s-Transform
Moment-Generating Property of the s-Transform
The s-Transforms of Some Well-Known PDFs
The s-Transform of the PDF of the Sum of Independent Random Variables
The z-Transform
Moment-Generating Property of the z-Transform
The z-Transform of the Bernoulli Distribution
The z-Transform of the Binomial Distribution
The z-Transform of the Geometric Distribution
The z-Transform of the Poisson Distribution
The z-Transform of the PMF of the Sum of Independent Random Variables
The z-Transform of the Pascal Distribution
Random Sum of Random Variables
Chapter Summary
Problems
Introduction to Random Processes
Introduction
Classification of Random Processes
Characterizing a Random Process
Mean and Autocorrelation Function of a Random Process
The Autocovariance Function of a Random Process
Crosscorrelation and Crosscovariance Functions
Review of Some Trigonometric Identities
Stationary Random Processes
Strict-Sense Stationary Processes
Wide-Sense Stationary Processes
Ergodic Random Processes
Power Spectral Density
White Noise
Discrete-Time Random Processes
Mean, Autocorrelation Function, and Autocovariance Function
Power Spectral Density
Sampling of Continuous-Time Processes
Chapter Summary
Problems
Linear Systems with Random Inputs
Introduction
Overview of Linear Systems with Deterministic Inputs
Linear Systems with Continuous-Time Random Inputs
Linear Systems with Discrete-Time Random Inputs
Autoregressive Moving Average Process
Moving Average Process
Autoregressive Process
ARMA Process
Chapter Summary
Problems
Some Models of Random Processes
Introduction
The Bernoulli Process
Random Walk
Gambler's Ruin
The Gaussian Process
White Gaussian Noise Process
Poisson Process
Counting Processes
Independent Increment Processes
Stationary Increments
Definitions of a Poisson Process
Interarrival Times for the Poisson Process
Conditional and Joint PMFs for Poisson Processes
Compound Poisson Process
Combinations of Independent Poisson Processes
Competing Independent Poisson Processes
Subdivision of a Poisson Process and the Filtered Poisson Process
Random Incidence
Nonhomogeneous Poisson Process
Markov Processes
Discrete-Time Markov Chains
State Transition Probability Matrix
The n-Step State Transition Probability
State Transition Diagrams
Classification of States
Limiting-State Probabilities
Doubly Stochastic Matrix
Continuous-Time Markov Chains
Birth and Death Processes
Gambler's Ruin as a Markov Chain
Chapter Summary
Problems
Introduction to Statistics
Introduction
Sampling Theory
The Sample Mean
The Sample Variance
Sampling Distributions
Estimation Theory
Point Estimate, Interval Estimate, and Confidence Interval
Maximum Likelihood Estimation
Minimum Mean Squared Error Estimation
Hypothesis Testing
Hypothesis Test Procedure
Type I and Type II Errors
One-Tailed and Two-Tailed Tests
Curve Fitting and Linear Regression
Chapter Summary
Problems
Table for the CDF of the Standard Normal Random Variable
Bibliography
Index
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