Introduction to probability and its applications.
Scheaffer, Richard L.
Introduction to probability and its applications. - Third edition / Richard L. Scheaffer, Linda Young. - x, 470 p. : ill. ; 24 cm.
Previous ed.: Belmont, Calif.: Duxbury, 1995. "Advanced series"--cover.
Includes bibliographical references and index.
Probability in the World Around Us -- Why Study Probability? -- Deterministic and Probabilistic Models -- Modeling Reality -- Deterministic Models -- Probabilistic Models -- Applications in Probability -- A Brief Historical Note -- A Look Ahead -- Foundations of Probability -- Understanding Randomness: An Intuitive Notion of Probability -- Randomness with Known Structure -- Randomness with Unknown Structure -- Sampling a Finite Universe -- Sample Space and Events -- Definition of Probability -- Counting Rules Useful in Probability -- More Counting Rules Useful in Probability -- Summary -- Conditional Probability and Independence -- Conditional Probability -- Independence -- Theorem of Total Probability and Bayes' Rule -- Odds, Odds Ratios, and Relative Risk -- Summary -- Discrete Probability Distributions -- Random Variables and Their Probability Distributions -- Expected Values of Random Variables -- The Bernoulli Distribution -- The Binomial Distribution -- Probability Function -- Mean and Variance -- History and Applications -- The Geometric Distribution -- Probability Function -- Mean and Variance -- An Alternate Parameterization: Number of Trials Versus Number of Failures -- The Negative Binomial Distribution -- Probability Function -- Mean and Variance -- An Alternate Parameterization: Number of Trials Versus Number of Failures -- History and Applications -- The Poisson Distribution -- Probability Function -- Mean and Variance -- History and Applications -- The Hypergeometric Distribution -- The Probability Function -- Mean and Variance -- History and Applications -- The Moment-generating Function -- The Probability-generating Function -- Markov Chains -- Summary -- Continuous Probability Distributions -- Continuous Random Variables and Their Probability Distributions -- Expected Values of Continuous Random Variables -- The Uniform Distribution -- Probability Density Function -- Mean and Variance -- History and Applications -- The Exponential Distribution -- Probability Density Function -- Mean and Variance -- Properties -- History and Applications -- The Gamma Distribution -- Probability Density Function -- Mean and Variance -- History and Applications -- The Normal Distribution -- The Normal Probability Density Function -- Mean and Variance -- Calculating Normal Probabilities -- Applications to Real Data -- Quantile-Quantile (Q-Q) Plots -- History -- The Beta Distribution -- Probability Density Function -- Mean and Variance -- H istory and Applications -- The Weibull Distribution -- Probability Density Function -- Mean and Variance -- History and Applications to Real Data -- Reliability -- Hazard Rate Function -- Series and Parallel Systems -- Redundancy -- Moment-generating Functions for Continuous Random Variables -- Expectations of Discontinuous Functions and Mixed Probability Distributions -- Summary -- Multivariate Probability Distributions -- Bivariate and Marginal Probability Distributions -- Conditional Probability Distributions -- Independent Random Variables -- Expected Values of Functions of Random Variables -- Conditional Expectations -- The Multinomial Distribution -- More on the Moment-Generating Function -- Compounding and Its Applications -- Summary -- Functions of Random Variables -- Introduction -- Functions of Discrete Random Variables -- Method of Distribution Functions -- Method of Transformations in One Dimension -- Method of Conditioning -- Method of Moment-Generating Functions -- Gamma Case -- Normal Case -- Normal and Gamma Relationships -- Method of Transformation - Two Dimensions -- Order Statistics -- Probability-Generating Functions: Applications to Random Sums of Random Variables -- Summary -- Some Approximations To Probability Distributions: Limit Theorems -- Introduction -- Convergence in Probability -- Convergence in Distribution -- The Central Limit Theorem -- Combination of Convergence in Probability and Convergence in Distribution -- Summary -- Extensions of Probability Theory -- The Poisson Process -- Birth and Death Processes: Biological Applications -- Queues: Engineering Applications -- Arrival Times for the Poisson Process -- Infinite Server Queue -- Renewal Theory: Reliability Applications -- Summary. 1. 2. 3. 4. 5. 6. 7. 8. 9.
9780534386719
Probabilities.
519.2
Introduction to probability and its applications. - Third edition / Richard L. Scheaffer, Linda Young. - x, 470 p. : ill. ; 24 cm.
Previous ed.: Belmont, Calif.: Duxbury, 1995. "Advanced series"--cover.
Includes bibliographical references and index.
Probability in the World Around Us -- Why Study Probability? -- Deterministic and Probabilistic Models -- Modeling Reality -- Deterministic Models -- Probabilistic Models -- Applications in Probability -- A Brief Historical Note -- A Look Ahead -- Foundations of Probability -- Understanding Randomness: An Intuitive Notion of Probability -- Randomness with Known Structure -- Randomness with Unknown Structure -- Sampling a Finite Universe -- Sample Space and Events -- Definition of Probability -- Counting Rules Useful in Probability -- More Counting Rules Useful in Probability -- Summary -- Conditional Probability and Independence -- Conditional Probability -- Independence -- Theorem of Total Probability and Bayes' Rule -- Odds, Odds Ratios, and Relative Risk -- Summary -- Discrete Probability Distributions -- Random Variables and Their Probability Distributions -- Expected Values of Random Variables -- The Bernoulli Distribution -- The Binomial Distribution -- Probability Function -- Mean and Variance -- History and Applications -- The Geometric Distribution -- Probability Function -- Mean and Variance -- An Alternate Parameterization: Number of Trials Versus Number of Failures -- The Negative Binomial Distribution -- Probability Function -- Mean and Variance -- An Alternate Parameterization: Number of Trials Versus Number of Failures -- History and Applications -- The Poisson Distribution -- Probability Function -- Mean and Variance -- History and Applications -- The Hypergeometric Distribution -- The Probability Function -- Mean and Variance -- History and Applications -- The Moment-generating Function -- The Probability-generating Function -- Markov Chains -- Summary -- Continuous Probability Distributions -- Continuous Random Variables and Their Probability Distributions -- Expected Values of Continuous Random Variables -- The Uniform Distribution -- Probability Density Function -- Mean and Variance -- History and Applications -- The Exponential Distribution -- Probability Density Function -- Mean and Variance -- Properties -- History and Applications -- The Gamma Distribution -- Probability Density Function -- Mean and Variance -- History and Applications -- The Normal Distribution -- The Normal Probability Density Function -- Mean and Variance -- Calculating Normal Probabilities -- Applications to Real Data -- Quantile-Quantile (Q-Q) Plots -- History -- The Beta Distribution -- Probability Density Function -- Mean and Variance -- H istory and Applications -- The Weibull Distribution -- Probability Density Function -- Mean and Variance -- History and Applications to Real Data -- Reliability -- Hazard Rate Function -- Series and Parallel Systems -- Redundancy -- Moment-generating Functions for Continuous Random Variables -- Expectations of Discontinuous Functions and Mixed Probability Distributions -- Summary -- Multivariate Probability Distributions -- Bivariate and Marginal Probability Distributions -- Conditional Probability Distributions -- Independent Random Variables -- Expected Values of Functions of Random Variables -- Conditional Expectations -- The Multinomial Distribution -- More on the Moment-Generating Function -- Compounding and Its Applications -- Summary -- Functions of Random Variables -- Introduction -- Functions of Discrete Random Variables -- Method of Distribution Functions -- Method of Transformations in One Dimension -- Method of Conditioning -- Method of Moment-Generating Functions -- Gamma Case -- Normal Case -- Normal and Gamma Relationships -- Method of Transformation - Two Dimensions -- Order Statistics -- Probability-Generating Functions: Applications to Random Sums of Random Variables -- Summary -- Some Approximations To Probability Distributions: Limit Theorems -- Introduction -- Convergence in Probability -- Convergence in Distribution -- The Central Limit Theorem -- Combination of Convergence in Probability and Convergence in Distribution -- Summary -- Extensions of Probability Theory -- The Poisson Process -- Birth and Death Processes: Biological Applications -- Queues: Engineering Applications -- Arrival Times for the Poisson Process -- Infinite Server Queue -- Renewal Theory: Reliability Applications -- Summary. 1. 2. 3. 4. 5. 6. 7. 8. 9.
9780534386719
Probabilities.
519.2