Rent 9780131867932 | Introduction to Mathematical Statistics and Its Applications, An | Larsen, Richard J.; Marx, Morris L. @knetbooks.com

Summary Table of Contents

Noted for its integration of real-world data and case studies, this guide offers sound coverage of the theoretical aspects of mathematical statistics. It demonstrates how and when to use statistical methods, while reinforcing the calculus that readers have already mastered. Presents standard statistical techniques in a mathematical context, allowing the reader to see the underlying hypotheses for the applications. Uses case studies and practical worked-out examples to motivate statistical reasoning and demonstrate the application of statistical... MORE

Preface

vii

Introduction

(20)

A Brief History

(9)

... MORE

(9)

A Chapter Summary

(1)

Probability

(107)

Introduction

(2)

Sample Spaces and the Algebra of Sets

(12)

The Probability Function

(6)

Conditional Probability

(27)

Independence

(16)

Combinatorics

(28)

Combinatorial Probability

113

(10)

Taking a Second Look at Statistics (Enumeration and Monte Carlo Techniques)

123

(5)

Random Variables

128

(146)

Introduction

129

(1)

Binomial and Hypergeometric Probabilities

130

(18)

Discrete Random Variables

148

(13)

Continuous Random Variables

161

(12)

Expected Values

173

(20)

The Variance

193

(10)

Joint Densities

203

(17)

Combining Random Variables

220

(6)

Further Properties of the Mean and Variance

226

(14)

Order Statistics

240

(9)

Conditional Densities

249

(8)

Moment-Generating Functions

257

(12)

Taking a Second Look at Statistics (Interpreting Means)

269

(5)

Appendix 3.A.1 MINITAB Applications

271

(3)

Special Distributions

274

(69)

Introduction

275

(1)

The Poisson Distribution

275

(17)

The Normal Distribution

292

(25)

The Geometric Distribution

317

(5)

The Negative Binomial Distribution

322

(5)

The Gamma Distribution

327

(6)

Taking a Second Look at Statistics (Monte Carlo Simulations)

333

(10)

Appendix 4.A.1 MINITAB Applications

337

(4)

Appendix 4.A.2 A Proof of the Central Limit Theorem

341

(2)

Estimation

343

(84)

Introduction

344

(2)

Estimating Parameters: The Method of Maximum Likelihood and the Method of Moments

346

(17)

Interval Estimation

363

(16)

Properties of Estimators

379

(15)

Minimum-Variance Estimators: The Cramer-Rao Lower Bound

394

(4)

Sufficient Estimators

398

(8)

Consistency

406

(4)

Bayesian Estimation

410

(13)

Taking a Second Look at Statistics (Revisiting the Margin of Error)

423

(4)

Appendix 5.A.1 MINITAB Applications

424

(3)

Hypothesis Testing

427

(42)

Introduction

428

(1)

The Decision Rule

428

(12)

Testing Binomial Data---H0: p = po

440

(6)

Type I and Type II Errors

446

(16)

A Notion of Optimality: The Generalized Likelihood Ratio

462

(4)

Taking a Second Look at Statistics (Statistical Significance versus ``Practical'' Significance)

466

(3)

The Normal Distribution

469

(53)

Introduction

470

(1)

Comparing Y-μ/σ/√n and Y-μ/S/√n

470

(3)

Deriving the Distribution of Y-μ/S/√n

473

(8)

Drawing Inferences About μ

481

(18)

Drawing Inferences About σ2

499

(10)

Taking a Second Look at Statistics (``Bad'' Estimators)

509

(13)

Appendix 7.A.1 MINITAB Applications

510

(4)

Appendix 7.A.2 Some Distribution Results for Y and S2

514

(2)

Appendix 7.A.3 A Proof of Theorem 7.5.2

516

(3)

Appendix 7.A.4 A Proof that the One-Sample t Test Is a GLRT

519

(3)

Types of Data: A Brief Overview

522

(31)

Introduction

523

(5)

Classifying Data

528

(24)

Taking a Second Look at Statistics (Samples Are Not ``Valid'')

552

(1)

Two-Sample Problems

553

(45)

Introduction

554

(1)

Testing H0: μx = μy -- The Two-Sample t Test

555

(13)

Testing H0: σ2/y -- The F Test

568

(8)

Binomial Data: Testing H0: px = py

576

(6)

Confidence Intervals for the Two-Sample Problem

582

(9)

Taking a Second Look at Statistics (Choosing Samples)

591

(7)

Appendix 9.A.1 A Derivation of the Two-Sample t Test (A Proof of Theorem 9.2.2)

593

(2)

Appendix 9.A.2 MINITAB Applications

595

(3)

Goodness-of-Fit Tests

598

(48)

Introduction

599

(1)

The Multinomial Distribution

599

(7)

Goodness-of-Fit Tests: All Parameters Known

606

(9)

Goodness-of-Fit Tests: Parameters Unknown

615

(12)

Contingency Tables

627

(13)

Taking a Second Look at Statistics (Outliers)

640

(6)

Appendix 10.A.1 MINITAB Applications

644

(2)

Regression

646

(86)

Introduction

647

(1)

The Method of Least Squares

647

(30)

The Linear Model

677

(25)

Covariance and Correlation

702

(15)

The Bivariate Normal Distribution

717

(8)

Taking a Second Look at Statistics (How Not to Interpret the Sample Correlation Coefficient)

725

(7)

Appendix 11.A.1 MINITAB Applications

726

(2)

Appendix 11.A.2 A Proof of Theorem 11.3.3

728

(4)

The Analysis of Variance

732

(40)

Introduction

733

(2)

The F Test

735

(12)

Multiple Comparisons: Tukey's Method

747

(4)

Testing Subhypotheses with Contrasts

751

(7)

Data Transformations

758

(3)

Taking a Second Look at Statistics (Putting the Subject of Statistics Together---The Contributions of Ronald A. Fisher)

761

(11)

Appendix 12.A.1 MINITAB Applications

762

(4)

Appendix 12.A.2 A Proof of Theorem 12.2.2

766

(1)

Appendix 12.A.3 The Distribution of SSTR/(k-1)/SSE/(n-k) When H1 Is True

767

(5)

Randomized Block Designs

772

(30)

Introduction

773

(1)

The F Test for a Randomized Block Design

774

(14)

The Paired t Test

788

(8)

Taking a Second Look at Statistics (Choosing Between a Two-Sample t Test and a Paired t Test)

796

(6)

Appendix 13.A.1 MINITAB Applications

800

(2)

Nonparametric Statistics

802

(48)

Introduction

803

(1)

The Sign Test

804

(6)

Wilcoxon Tests

810

(16)

The Kruskal-Wallis Test

826

(6)

The Friedman Test

832

(3)

Testing for Randomness

835

(6)

Taking a Second Look at Statistics (Comparing Parametric and Nonparametric Procedures)

841

(9)

Appendix 14.A.1 MINITAB Applications

846

(4)

Appendix: Statistical Tables

850

(26)

Answers to Selected Odd-Numbered Questions

876

(31)

Bibliography

907

(8)

Index

915

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