Fundamentals of applied probability and random processes / Oliver Ibe.

Format:

Book

Author/Creator:

Ibe, Oliver C. (Oliver Chukwudi), 1947- author.

Language:

English

Subjects (All):

Probabilities.

Physical Description:

1 online resource (457 p.)

Edition:

Second edition.

Place of Publication:

San Diego, California ; Waltham, [Massachusetts] : Academic Press, 2014

Language Note:

English

System Details:

text file

Summary:

e it ideal for the classroom or for self-study. The book: 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 a 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). -- Edited summary from book

Contents:

Front Cover

Fundamentals of Applied Probability and Random Processes

Copyright

Contents

Acknowledgment

Preface to the Second Edition

Preface to First Edition

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. Information Theory

1.4.2. Reliability Engineering

1.4.3. Quality Control

1.4.4. Channel Noise

1.4.5. 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. The Fundamental Counting Rule

1.10.8. Applications of Combinations in Probability

1.11. Reliability Applications

1.12. Chapter Summary

1.13. Problems

Section 1.2. Sample Space and Events

Section 1.3. Definitions of Probability

Section 1.5. Elementary Set Theory

Section 1.6. Properties of Probability

Section 1.7. Conditional Probability

Section 1.8. Independent Events

Section 1.10. Combinatorial Analysis

Section 1.11. Reliability Applications

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. Chapter Summary

2.8. Problems

Section 2.4. Distribution Functions

Section 2.5. Discrete Random Variables

Section 2.6. Continuous Random Variables

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 Markov Inequality

3.7. The Chebyshev Inequality

3.8. Chapter Summary

3.9. Problems

Section 3.2. Expected Values

Section 3.4. Moments of Random Variables and the Variance

Section 3.5. Conditional Expectations

Sections 3.6 and 3.7. Markov and Chebyshev Inequalities

Chapter 4: Special Probability Distributions

4.1. Introduction

4.2. The Bernoulli Trial and Bernoulli Distribution

4.3. Binomial Distribution

4.4. Geometric Distribution

4.4.1. CDF of the Geometric Distribution

4.4.2. Modified Geometric Distribution

4.4.3. ``Forgetfulness´´ Property of the Geometric Distribution

4.5. Pascal Distribution

4.5.1. Distinction Between Binomial and Pascal Distributions

4.6. Hypergeometric Distribution

4.7. Poisson Distribution

4.7.1. Poisson Approximation of the Binomial Distribution

4.8. Exponential Distribution

4.8.1. ``Forgetfulness´´ Property of the Exponential Distribution

4.8.2. Relationship between the Exponential and Poisson Distributions

4.9. Erlang Distribution

4.10. Uniform Distribution

4.10.1. The Discrete Uniform Distribution

4.11. Normal Distribution

4.11.1. Normal Approximation of the Binomial Distribution

4.11.2. The Error Function

4.11.3. The Q-Function

4.12. The Hazard Function

4.13. Truncated Probability Distributions

4.13.1. Truncated Binomial Distribution.

4.13.2. Truncated Geometric Distribution

4.13.3. Truncated Poisson Distribution

4.13.4. Truncated Normal Distribution

4.14. Chapter Summary

4.15. Problems

Section 4.3. Binomial Distribution

Section 4.4. Geometric Distribution

Section 4.5. Pascal Distribution

Section 4.6. Hypergeometric Distribution

Section 4.7. Poisson Distribution

Section 4.8. Exponential Distribution

Section 4.9. Erlang Distribution

Section 4.10. Uniform Distribution

Section 4.11. Normal Distribution

Chapter 5: Multiple Random Variables

5.1. Introduction

5.2. Joint CDFs of Bivariate Random Variables

5.2.1. Properties of the Joint CDF

5.3. Discrete Bivariate Random Variables

5.4. Continuous Bivariate Random Variables

5.5. Determining Probabilities from a Joint CDF

5.6. Conditional Distributions

5.6.1. Conditional PMF for Discrete Bivariate Random Variables

5.6.2. Conditional PDF for Continuous Bivariate Random Variables

5.6.3. Conditional Means and Variances

5.6.4. Simple Rule for Independence

5.7. Covariance and Correlation Coefficient

5.8. Multivariate Random Variables

5.9. Multinomial Distributions

5.10. Chapter Summary

5.11. Problems

Section 5.3. Discrete Bivariate Random Variables

Section 5.4. Continuous Bivariate Random Variables

Section 5.6. Conditional Distributions

Section 5.7. Covariance and Correlation Coefficient

Section 5.9. Multinomial Distributions

Chapter 6: Functions of Random Variables

6.1. Introduction

6.2. Functions of One Random Variable

6.2.1. Linear Functions

6.2.2. Power Functions

6.3. Expectation of a Function of One Random Variable

6.3.1. Moments of a Linear Function

6.3.2. Expected Value of a Conditional Expectation

6.4. Sums of Independent Random Variables

6.4.1. Moments of the Sum of Random Variables.

6.4.2. Sum of Discrete Random Variables

6.4.3. Sum of Independent Binomial Random Variables

6.4.4. Sum of Independent Poisson Random Variables

6.4.5. The Spare Parts Problem

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

6.8.1. Application of the Transformation Method

6.9. Laws of Large Numbers

6.10. The Central Limit Theorem

6.11. Order Statistics

6.12. Chapter Summary

6.13. Problems

Section 6.2. Functions of One Random Variable

Section 6.4. Sums of Random Variables

Sections 6.4 and 6.5. Maximum and Minimum of Independent Random Variables

Section 6.8. Two Functions of Two Random Variables

Section 6.10. The Central Limit Theorem

Section 6.11. Order Statistics

Chapter 7: Transform Methods

7.1. Introduction

7.2. The Characteristic Function

7.2.1. Moment-Generating Property of the Characteristic Function

7.2.2. Sums of Independent Random Variables

7.2.3. The Characteristic Functions of Some Well-Known Distributions

7.3. The s-Transform

7.3.1. Moment-Generating Property of the s-Transform

7.3.2. The s-Transform of the PDF of the Sum of Independent Random Variables

7.3.3. The s-Transforms of Some Well-Known PDFs

7.4. The z-Transform

7.4.1. Moment-Generating Property of the z-Transform

7.4.2. The z-Transform of the PMF of the Sum of Independent Random Variables

7.4.3. The z-Transform of Some Well-Known PMFs

7.5. Random Sum of Random Variables

7.6. Chapter Summary

7.7. Problems

Section 7.2. Characteristic Functions

Section 7.3. s-Transforms

Section 7.4. z-Transforms

Section 7.5. Random Sum of Random Variables

Chapter 8: Introduction to Descriptive Statistics

8.1. Introduction.

8.2. Descriptive Statistics

8.3. Measures of Central Tendency

8.3.1. Mean

8.3.2. Median

8.3.3. Mode

8.4. Measures of Dispersion

8.4.1. Range

8.4.2. Quartiles and Percentiles

8.4.3. Variance

8.4.4. Standard Deviation

8.5. Graphical and Tabular Displays

8.5.1. Dot Plots

8.5.2. Frequency Distribution

8.5.3. Histograms

8.5.4. Frequency Polygons

8.5.5. Bar Graphs

8.5.6. Pie Chart

8.5.7. Box and Whiskers Plot

8.6. Shape of Frequency Distributions: Skewness

8.7. Shape of Frequency Distributions: Peakedness

8.8. Chapter Summary

8.9. Problems

Section 8.3. Measures of Central Tendency

Section 8.4. Measures of Dispersion

Section 8.6. Graphical Displays

Section 8.7. Shape of Frequency Distribution

Chapter 9: Introduction to Inferential Statistics

9.1. Introduction

9.2. Sampling Theory

9.2.1. The Sample Mean

9.2.2. The Sample Variance

9.2.3. Sampling Distributions

9.3. Estimation Theory

9.3.1. Point Estimate, Interval Estimate, and Confidence Interval

9.3.2. Maximum Likelihood Estimation

9.3.3. Minimum Mean Squared Error Estimation

9.4. Hypothesis Testing

9.4.1. Hypothesis Test Procedure

9.4.2. Type I and Type II Errors

9.4.3. One-Tailed and Two-Tailed Tests

9.5. Regression Analysis

9.6. Chapter Summary

9.7. Problems

Section 9.2. Sampling Theory

Section 9.3. Estimation Theory

Section 9.4. Hypothesis Testing

Section 9.5. Regression Analysis

Chapter 10: Introduction to Random Processes

10.1. Introduction

10.2. Classification of Random Processes

10.3. Characterizing a Random Process

10.3.1. Mean and Autocorrelation Function

10.3.2. The Autocovariance Function

10.4. Crosscorrelation and Crosscovariance Functions

10.4.1. Review of Some Trigonometric Identities

10.5. Stationary Random Processes.

10.5.1. Strict-Sense Stationary Processes.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9780128010358

0128010355

OCLC:

881820918