http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
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 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). --
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
Includes bibliographical references and index.