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Fundamentals of applied probability and random processes /

This revised edition 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. Its clear writing style and homework problems make it ideal for the classroom or for...

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Detalles Bibliográficos
Clasificación:	Libro Electrónico
Autor principal:	Ibe, Oliver C. (Oliver Chukwudi), 1947- (Autor)
Formato:	Electrónico eBook
Idioma:	Inglés
Publicado:	San Diego, CA : Academic Press, 2014.
Edición:	2nd edition.
Temas:	Probabilities. Probability Probabilit�es. probability. MATHEMATICS > Applied. MATHEMATICS > Probability & Statistics > General. Probabilities
Acceso en línea:	Texto completo

Tabla de Contenidos:

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
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
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
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
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
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
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 Welt-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
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
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
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
10.5.2.Wide-Sense Stationary Processes
10.6.Ergodic Random Processes
10.7.Power Spectral Density
10.7.1.White Noise
10.8.Discrete-Time Random Processes
10.8.1.Mean, Autocorrelation Function and Autocovariance Function
10.8.2.Power Spectral Density of a Random Sequence
10.8.3.Sampling of Continuous-Time Processes
10.9.Chapter Summary
10.10.Problems
Section 10.3 Mean, Autocorrelation Function and Autocovariance Function
Section 10.4 Crosscorrelation and Crosscovariance Functions
Section 10.5 Wide-Sense Stationary Processes
Section 10.6 Ergodic Random Processes
Section 10.7 Power Spectral Density
Section 10.8 Discrete-Time Random Processes
11.1.Introduction
11.2.Overview of Linear Systems with Deterministic Inputs
11.3.Linear Systems with Continuous-Time Random Inputs
11.4.Linear Systems with Discrete-Time Random Inputs
11.5.Autoregressive Moving Average Process
11.5.1.Moving Average Process
11.5.2.Autoregressive Process
11.5.3.ARMA Process
11.6.Chapter Summary
11.7.Problems
Section 11.2 Linear Systems with Deterministic Input
Section 11.3 Linear Systems with Continuous Random Input
Section 11.4 Linear Systems with Discrete Random Input
Section 11.5 Autoregressive Moving Average Processes
12.1.Introduction
12.2.The Bernoulli Process
12.3.Random Walk Process
12.3.1.Symmetric Simple Random Walk

Fundamentals of applied probability and random processes /

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