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Modern Mathematical Statistics with Applications (with CD-ROM)

by: Devore, Jay L.; Berk, Kenneth N.

Modern Mathematical Statistics with Applications (with CD-ROM)

by: Devore, Jay L.; Berk, Kenneth N.

ISBN 13:
9780534404734
ISBN 10:
0534404731
Edition: CD
Format: Hardcover
Copyright: 01/06/2006
Publisher: Cengage Learning
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Summary

Many mathematical statistics texts are heavily oriented toward a rigorous mathematical development of probability and statistics, without emphasizing contemporary statistical practice. MODERN MATHEMATICAL STATISTICS WITH APPLICATIONS strikes a balance between mathematical foundations and statistical practice. Accomplished authors Jay Devore and Ken Berk first engage students with real-life problems and scenarios and then provide them with both foundational context and theory. This book follows the spirit of the Committee on the Undergraduate Program in Mathematics (CUPM) recommendation that every math student should study statistics and probability with an emphasis on data analysis.

Preface

viii

Overview and Descriptive Statistics

(48)

Introduction

(1)

Populations and Samples

(7)

Pictorial and Tabular Methods in Descriptive Statistics

(16)

Measures of Location

(8)

Measures of Variability

(16)

Probability

(45)

Introduction

(1)

Sample Spaces and Events

(6)

Axioms, Interpretations, and Properties of Probability

(9)

Counting Techniques

(8)

Conditional Probability

(10)

Independence

(11)

Discrete Random Variables and Probability Distributions

(60)

Introduction

(1)

Random Variables

(4)

Probability Distributions for Discrete Random Variables

(10)

Expected Values of Discrete Random Variables

109

(9)

Moments and Moment Generating Functions

118

(7)

The Binomial Probability Distribution

125

(9)

*Hypergeometric and Negative Binomial Distributions

134

(8)

*The Poisson Probability Distribution

142

(12)

Continuous Random Variables and Probability Distributions

154

(75)

Introduction

154

(1)

Probability Density Functions and Cumulative Distribution Functions

155

(12)

Expected Values and Moment Generating Functions

167

(8)

The Normal Distribution

175

(15)

*The Gamma Distribution and Its Relatives

190

(8)

*Other Continuous Distributions

198

(8)

*Probability Plots

206

(10)

*Transformations of a Random Variable

216

(13)

Joint Probability Distributions

229

(49)

Introduction

229

(1)

Jointly Distributed Random Variables

230

(12)

Expected Values, Covariance, and Correlation

242

(7)

*Conditional Distributions

249

(13)

*Transformations of Random Variables

262

(5)

*Order Statistics

267

(11)

Statistics and Sampling Distributions

278

(47)

Introduction

278

(1)

Statistics and Their Distributions

279

(12)

The Distribution of the Sample Mean

291

(9)

The Distribution of a Linear Combination

300

(9)

Distributions Based on a Normal Random Sample

309

(16)

Appendix: Proof of the Central Limit Theorem

323

(2)

Point Estimation

325

(50)

Introduction

325

(1)

General Concepts and Criteria

326

(18)

*Methods of Point Estimation

344

(11)

*Sufficiency

355

(9)

*Information and Efficiency

364

(11)

Statistical Intervals Based on a Single Sample

375

(42)

Introduction

375

(1)

Basic Properties of Confidence Intervals

376

(9)

Large-Sample Confidence Intervals for a Population Mean and Proportion

385

(8)

Intervals Based on a Normal Population Distribution

393

(8)

*Confidence Intervals for the Variance and Standard Deviation of a Normal Population

401

(3)

*Bootstrap Confidence Intervals

404

(13)

Tests of Hypotheses Based on a Single Sample

417

(55)

Introduction

417

(1)

Hypotheses and Test Procedures

418

(10)

Tests About a Population Mean

428

(14)

Tests Concerning a Population Proportion

442

(6)

P-Values

448

(8)

*Some Comments on Selecting a Test Procedure

456

(16)

Inferences Based on Two Samples

472

(67)

Introduction

472

(1)

z Tests and Confidence Intervals for a Difference Between Two Population Means

473

(14)

The Two-Sample t Test and Confidence Interval

487

(10)

Analysis of Paired Data

497

(10)

Inferences About Two Population Proportions

507

(8)

*Inferences About Two Population Variances

515

(5)

*Comparisons Using the Bootstrap and Permutation Methods

520

(19)

The Analysis of Variance

539

(60)

Introduction

539

(1)

Single-Factor ANOVA

540

(12)

*Multiple Comparisons in ANOVA

552

(8)

*More on Single-Factor ANOVA

560

(10)

*Two-Factor ANOVA with Kij = 1

570

(14)

*Two-Factor ANOVA with Kij > 1

584

(15)

Regression and Correlation

599

(108)

Introduction

599

(1)

The Simple Linear and Logistic Regression Models

600

(11)

Estimating Model Parameters

611

(15)

Inferences About the Regression Coefficient β1

626

(14)

Inferences Concerning μγ, x* and the Prediction of Future Y Values

640

(8)

Correlation

648

(12)

*Aptness of the Model and Model Checking

660

(8)

*Multiple Regression Analysis

668

(21)

*Regression with Matrices

689

(18)

Goodness-of-Fit Tests and Categorical Data Analysis

707

(36)

Introduction

707

(1)

Goodness-of-Fit Tests When Category Probabilities Are Completely Specified

708

(8)

*Goodness-of-Fit Tests for Composite Hypotheses

716

(13)

Two-Way Contingency Tables

729

(14)

Alternative Approaches to Inference

743

(38)

Introduction

743

(1)

*The Wilcoxon Signed-Rank Test

744

(8)

*The Wilcoxon Rank-Sum Test

752

(5)

*Distribution-Free Confidence Intervals

757

(5)

*Bayesian Methods

762

(8)

*Sequential Methods

770

(11)

Appendix Tables

781

(28)

A.1 Cumulative Binomial Probabilities

782

(2)

A.2 Cumulative Poisson Probabilities

784

(2)

A.3 Standard Normal Curve Areas

786

(2)

A.4 The Incomplete Gamma Function

788

(1)

A.5 Critical Values for t Distributions

789

(1)

A.6 Tolerance Critical Values for Normal Population Distributions

790

(1)

A.7 Critical Values for Chi-Squared Distributions

791

(1)

A.8 t Curve Tail Areas

792

(2)

A.9 Critical Values for F Distributions

794

(6)

A.10 Critical Values for Studentized Range Distributions

800

(1)

A.11 Chi-Squared Curve Tail Areas

801

(2)

A.12 Critical Values for the Ryan--Joiner Test of Normality

803

(1)

A.13 Critical Values for the Wilcoxon Signed-Rank Test

804

(1)

A.14 Critical Values for the Wilcoxon Rank-Sum Test

805

(1)

A.15 Critical Values for the Wilcoxon Signed-Rank Interval

806

(1)

A.16 Critical Values for the Wilcoxon Rank-Sum Interval

807

(1)

A.17 β Curves for t Tests

808

(1)

Answers to Odd-Numbered Exercises

809

(20)

Index

829

Amazon no longer offers textbook rentals. We do!

Modern Mathematical Statistics with Applications (with CD-ROM)

Modern Mathematical Statistics with Applications (with CD-ROM)

9780534404734

0534404731

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Modern Mathematical Statistics with Applications (with CD-ROM)

Modern Mathematical Statistics with Applications (with CD-ROM)

9780534404734

0534404731

Summary

Table of Contents

Supplemental Materials

Write a Review

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