Mathematical Statistics with Applications – Dennis D. Wackerly, William Mendenhall, Richard L. Scheaffer – 7th Edition

Descripción

con aplicaciones se escribió para su uso con una secuencia de cursos de 1 año de pregrado (9 cuartos de hora o 6 semestres) sobre estadísticas matemáticas. La intención del texto es presentar una base sólida de pregrado en teoría , mientras proporciona una indicación de la relevancia e importancia de la teoría para resolver problemas prácticos en el mundo real.

Creemos que un curso de este tipo es adecuado para la mayoría de las disciplinas de pregrado, incluidas las matemáticas, donde el contacto con las aplicaciones puede brindar una experiencia refrescante y motivadora. El único prerrequisito matemático es un profundo del cálculo universitario de primer año, que incluye sumas de series infinitas, diferenciación e integración simple y doble.

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  • Preface
    Note to the Student
    1 What Is Statistics?
    1.1 Introduction
    1.2 Characterizing a Set of Measurements: Graphical Methods
    1.3 Characterizing a Set of Measurements: Numerical Methods
    1.4 How Inferences Are Made
    1.5 Theory and Reality
    1.6 Summary
    2 Probability
    2.1 Introduction
    2.2 Probability and Inference
    2.3 A Review of Set Notation
    2.4 A Probabilistic Model for an Experiment: The Discrete Case
    2.5 Calculating the Probability of an Event: The Sample-Point Method
    2.6 Tools for Counting Sample Points
    2.7 Conditional Probability and the Independence of Events
    2.8 Two Laws of Probability
    2.9 Calculating the Probability of an Event: The Event-Composition Method
    2.10 The Law of Total Probability and Bayes’ Rule
    2.11 Numerical Events and Random Variables
    2.12 Random Sampling
    2.13 Summary
    3 Discrete Random Variables and Their Probability Distributions
    3.1 Basic Definition
    3.2 The Probability Distribution for a Discrete Random Variable
    3.3 The Expected Value of a Random Variable or a Function of a Random Variable
    3.4 The Binomial Probability Distribution
    3.5 The Geometric Probability Distribution
    3.6 The Negative Binomial Probability Distribution (Optional)
    3.7 The Hypergeometric Probability Distribution
    3.8 The Poisson Probability Distribution
    3.9 Moments and Moment-Generating Functions
    3.10 Probability-Generating Functions (Optional)
    3.11 Tchebysheff’s Theorem
    3.12 Summary
    4 Continuous Variables and Their Probability Distributions
    4.1 Introduction
    4.2 The Probability Distribution for a Continuous Random Variable
    4.3 Expected Values for Continuous Random Variables
    4.4 The Uniform Probability Distribution
    4.5 The Normal Probability Distribution
    4.6 The Gamma Probability Distribution
    4.7 The Beta Probability Distribution
    4.8 Some General Comments
    4.9 Other Expected Values
    4.10 Tchebysheff’s Theorem
    4.11 Expectations of Discontinuous Functions and Mixed Probability Distributions (Optional)
    4.12 Summary
    5 Multivariate Probability Distributions
    5.1 Introduction
    5.2 Bivariate and Multivariate Probability Distributions
    5.3 Marginal and Conditional Probability Distributions
    5.4 Independent Random Variables
    5.5 The Expected Value of a Function of Random Variables
    5.6 Special Theorems
    5.7 The Covariance of Two Random Variables
    5.8 The Expected Value and Variance of Linear Functions of Random Variables
    5.9 The Multinomial Probability Distribution
    5.10 The Bivariate Normal Distribution (Optional)
    5.11 Conditional Expectations
    5.12 Summary
    6 Functions of Random Variables
    6.1 Introduction
    6.2 Finding the Probability Distribution of a Function
    of Random Variables
    6.3 The Method of Distribution Functions
    6.4 The Method of Transformations
    6.5 The Method of Moment-Generating Functions
    6.6 Multivariable Transformations Using Jacobians (Optional)
    6.7 Order Statistics
    6.8 Summary
    7 Sampling Distributions and the Central
    Limit Theorem
    7.1 Introduction
    7.2 Sampling Distributions Related to the Normal Distribution
    7.3 The Central Limit Theorem
    7.4 A Proof of the Central Limit Theorem (Optional)
    7.5 The Normal Approximation to the Binomial Distribution
    7.6 Summary
    8 Estimation
    8.1 Introduction
    8.2 The Bias and Mean Square Error of Point Estimators
    8.3 Some Common Unbiased Point Estimators
    8.4 Evaluating the Goodness of a Point Estimator
    8.5 Confidence Intervals
    8.6 Large-Sample Confidence Intervals
    8.7 Selecting the Sample Size
    8.8 Small-Sample Confidence Intervals for µ and µ1 ? µ2
    8.9 Confidence Intervals for ?2
    8.10 Summary
    9 Properties of Point Estimators and Methods of Estimation
    9.1 Introduction
    9.2 Relative Efficiency
    9.3 Consistency
    9.4 Sufficiency
    9.5 The Rao–Blackwell Theorem and Minimum-Variance Unbiased Estimation
    9.6 The Method of Moments
    9.7 The Method of Maximum Likelihood
    9.8 Some Large-Sample Properties of Maximum-Likelihood Estimators (Optional)
    9.9 Summary
    10 Hypothesis Testing
    10.1 Introduction
    10.2 Elements of a Statistical Test
    10.3 Common Large-Sample Tests
    10.4 Calculating Type II Error Probabilities and Finding the Sample Size for Z Tests
    10.5 Relationships Between Hypothesis-Testing Procedures and Confidence Intervals
    10.6 Another Way to Report the Results of a Statistical Test: Attained Significance Levels, or p-Values
    10.7 Some Comments on the Theory of Hypothesis Testing
    10.8 Small-Sample Hypothesis Testing for µ and µ1 ? µ2
    10.9 Testing Hypotheses Concerning Variances
    10.10 Power of Tests and the Neyman–Pearson Lemma
    10.11 Likelihood Ratio Tests
    10.12 Summary
    11 Linear Models and Estimation by Least Squares
    11.1 Introduction
    11.2 Linear Statistical Models
    11.3 The Method of Least Squares
    11.4 Properties of the Least-Squares Estimators: Simple Linear Regression
    11.5 Inferences Concerning the Parameters ?i
    11.6 Inferences Concerning Linear Functions of the Model Parameters: Simple Linear Regression
    11.7 Predicting a Particular Value of Y by Using Simple Linear Regression
    11.8 Correlation
    11.9 Some Practical Examples
    11.10 Fitting the Linear Model by Using Matrices
    11.11 Linear Functions of the Model Parameters: Multiple Linear Regression
    11.12 Inferences Concerning Linear Functions of the Model Parameters: Multiple Linear Regression
    11.13 Predicting a Particular Value of Y by Using Multiple Regression
    11.14 A Test for H0 : ?g+1 = ?g+2 =···= ?k = 0
    11.15 Summary and Concluding Remarks
    12 Considerations in Designing Experiments
    12.1 The Elements Affecting the Information in a Sample
    12.2 Designing Experiments to Increase Accuracy
    12.3 The Matched-Pairs Experiment
    12.4 Some Elementary Experimental Designs
    12.5 Summary
    13 The Analysis of Variance
    13.1 Introduction
    13.2 The Analysis of Variance Procedure
    13.3 Comparison of More Than Two Means: Analysis of Variance for a One-Way Layout
    13.4 An Analysis of Variance Table for a One-Way Layout
    13.5 A Statistical Model for the One-Way Layout
    13.6 Proof of Additivity of the Sums of Squares and E(MST) for a One-Way Layout (Optional)
    13.7 Estimation in the One-Way Layout
    13.8 A Statistical Model for the Randomized Block Design
    13.9 The Analysis of Variance for a Randomized Block Design
    13.10 Estimation in the Randomized Block Design
    13.11 Selecting the Sample Size
    13.12 Simultaneous Confidence Intervals for More Than One Parameter
    13.13 Analysis of Variance Using Linear Models
    13.14 Summary
    14 Analysis of Categorical Data
    14.1 A Description of the Experiment
    14.2 The Chi-Square Test
    14.3 A Test of a Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-Fit Test
    14.4 Contingency Tables
    14.5 r × c Tables with Fixed Row or Column Totals
    14.6 Other Applications
    14.7 Summary and Concluding Remarks
    15 Nonparametric Statistics
    15.1 Introduction
    15.2 A General Two-Sample Shift Model
    15.3 The Sign Test for a Matched-Pairs Experiment
    15.4 The Wilcoxon Signed-Rank Test for a Matched-Pairs Experiment
    15.5 Using Ranks for Comparing Two Population Distributions:Independent Random Samples
    15.6 The Mann–Whitney U Test: Independent Random Samples
    15.7 The Kruskal–Wallis Test for the One-Way Layout
    15.8 The Friedman Test for Randomized Block Designs
    15.9 The Runs Test: A Test for Randomness
    15.10 Rank Correlation Coefficient
    15.11 Some General Comments on Nonparametric Statistical Tests
    16 Introduction to Bayesian Methods for Inference
    16.1 Introduction
    16.2 Bayesian Priors, Posteriors, and Estimators
    16.3 Bayesian Credible Intervals
    16.4 Bayesian Tests of Hypotheses
    16.5 Summary and Additional Comments
    Appendix 1 Matrices and Other Useful
    Mathematical Results
    A1.1 Matrices and Matrix Algebra
    A1.2 Addition of Matrices
    A1.3 Multiplication of a Matrix by a Real Number
    A1.4 Matrix Multiplication
    A1.5 Identity Elements
    A1.6 The Inverse of a Matrix
    A1.7 The Transpose of a Matrix
    A1.8 A Matrix Expression for a System of Simultaneous Linear Equations
    A1.9 Inverting a Matrix
    A1.10 Solving a System of Simultaneous Linear Equations
    A1.11 Other Useful Mathematical Results
    Appendix 2 Common Probability Distributions, Means, Variances, and Moment-Generating Functions
    Table 1 Discrete Distributions
    Table 2 Continuous Distributions
    Appendix 3 Tables
    Table 1 Binomial Probabilities
    Table 2 Table of e?x
    Table 3 Poisson Probabilities
    Table 4 Normal Curve Areas
    Table 5 Percentage Points of the t Distributions
    Table 6 Percentage Points of the ?2 Distributions
    Table 7 Percentage Points of the F Distributions
    Table 8 Distribution Function of U
    Table 9 Critical Values of T in the Wilcoxon Matched-Pairs, Signed-Ranks Test, n = 5(1)50
    Table 10 Distribution of the Total Number of Runs R in Samples of Size (n1, n2), P(R ? a)
    Table 11 Critical Values of Spearman’s Rank Correlation Coefficient
    Table 12 Random Numbers
    Answers to Exercises
    Index
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