Fundamentals of applied probability and random processes

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...

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Detalles Bibliográficos
Otros Autores:	Ibe, Oliver C. 1947- author (author)
Formato:	Libro electrónico
Idioma:	Inglés
Publicado:	San Diego, California ; Waltham, [Massachusetts] : Academic Press 2014
Edición:	Second edition
Materias:	Probabilities.
Ver en Biblioteca Universitat Ramon Llull:	https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009629528706719

Tabla de Contenidos:

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.

Fundamentals of applied probability and random processes

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