Rent 9780139223037 | Introduction to Mathematical Statistics and Its Applications, An | Larsen, Richard J.; Marx, Morris L. @knetbooks.com

Summary Table of Contents

Using high-quality, real-world case studies and examples, this introduction to mathematical statistics shows how to use statistical methods and when to use them. This book can be used as a brief introduction to design of experiments. This successful, calculus-based book of probability and statistics, was one of the first to make real-world applications an integral part of motivating discussion. The number of problem sets has increased in all sections. Some sections include almost 50% new problems, while the most popular case studies remain. Fo... MORE

Preface

Introduction

(19)

A Brief History

(9)

S... MORE

(7)

A Chapter Summary

(2)

Probability

(99)

Introduction

(1)

Sample Spaces and the Algebra of Sets

(8)

The Probability Function

(7)

Discrete Probability Functions

(6)

Continuous Probability Functions

(9)

Conditional Probability

(19)

Independence

(9)

Repeated Independent Trials

(7)

Combinatorics

(23)

Combinatorial Probability

109

(10)

Random Variables

119

(126)

Introduction

120

(1)

The Probability Density Function

121

(7)

The Hypergeometric and Binomial Distributions

128

(16)

The Cumulative Distribution Function

144

(9)

Joint Densities

153

(14)

Independent Random Variables

167

(3)

Combining and Transforming Random Variables

170

(10)

Order Statistics

180

(5)

Conditional Densities

185

(5)

Expected Values

190

(12)

Properties of Expected Values

202

(16)

The Variance

218

(4)

Properties of Variances

222

(7)

Chebyshev's Inequality

229

(3)

Higher Moments

232

(4)

Moment-Generating Functions

236

(9)

Appendix 3.A.1 MINITAB Applications

243

(2)

Special Distributions

245

(62)

Introduction

246

(1)

The Poisson Distribution

246

(17)

The Normal Distribution

263

(23)

The Geometric Distribution

286

(6)

The Negative Binomial Distribution

292

(4)

The Gamma Distribution

296

(11)

Appendix 4.A.1 MINITAB Applications

301

(4)

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

305

(2)

Estimation

307

(57)

Introduction

308

(2)

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

310

(13)

Interval Estimation

323

(14)

Properties of Estimators

337

(13)

Minimum-Variance Estimators: The Cramer-Rao Lower Bound

350

(3)

Sufficiency

353

(5)

Consistency

358

(6)

Appendix 5.A.1 MINITAB Applications

361

(3)

Hypothesis Testing

364

(37)

Introduction

365

(1)

The Decision Rule

365

(10)

Testing Binomial Data---H0: p = p0

375

(7)

Type I and Type II Errors

382

(15)

A Notion of Optimality: the Generalized Likelihood Ratio

397

(4)

The Normal Distribution

401

(61)

Introduction

402

(1)

Point Estimates for μ and σ2

402

(8)

The X2 Distribution; Inferences about σ2

410

(11)

The F and t Distributions

421

(9)

Drawing Inferences about μ

430

(32)

Appendix 7.A.1 MINITAB Applications

451

(4)

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

455

(2)

Appendix 7.A.3 A Proof of Theorem 7.3.5

457

(2)

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

459

(3)

Types of Data: A Brief Overview

462

(22)

Introduction

463

(5)

Classifying Data

468

(16)

Two-Sample Problems

484

(41)

Introduction

485

(1)

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

486

(11)

Testing H0: σ2x = σ2y---the F Test

497

(8)

Binomial Data: Testing H0: px = py

505

(5)

Confidence Intervals for the Two-Sample Problem

510

(15)

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

518

(2)

Appendix 9.A.2 Power Calculations for a Two-Sample t Test

520

(3)

Appendix 9.A.3 MINITAB Applications

523

(2)

Goodness-of-Fit Tests

525

(33)

Introduction

526

(1)

The Multinomial Distribution

526

(6)

Goodness-of-Fit Tests: All Parameters Known

532

(8)

Goodness-of-Fit Tests: Parameters Unknown

540

(8)

Contingency Tables

548

(10)

Appendix 10.A.1 MINITAB Applications

556

(2)

Regression

558

(75)

Introduction

559

(1)

The Method of Least Squares

559

(25)

The Linear Model

584

(22)

Covariance and Correlation

606

(14)

The Bivariate Normal Distribution

620

(13)

Appendix 11.A.1 MINITAB Applications

627

(2)

Appendix 11.A.2 A Proof of Theorem 11.3.3

629

(4)

The Analysis of Variance

633

(34)

Introduction

634

(2)

The F Test

636

(10)

Multiple Comparisons: Tukey's Method

646

(4)

Testing Subhypotheses with Orthogonal Contrasts

650

(6)

Data Transformations

656

(11)

Appendix 12.A.1 MINITAB Applications

659

(3)

Appendix 12.A.2 A Proof of Theorem 12.2.2

662

(1)

Appendix 12.A.3 The Distribution of When H1 is True

662

(5)

Randomized Block Designs

667

(20)

Introduction

668

(1)

The F Test for a Randomized Block Design

669

(13)

The Paired t Test

682

(5)

Appendix 13.A.1 MINITAB Applications

685

(2)

Nonparametric Statistics

687

(28)

Introduction

688

(1)

The Sign Test

689

(3)

The Wilcoxon Signed Rank Test

692

(11)

The Kruskal-Wallis Test

703

(4)

The Friedman Test

707

(8)

Appendix 14.A.1 MINITAB Applications

710

(5)

Appendix: Statistical Tables

715

(27)

Answers to Selected Odd-Numbered Questions

742

(34)

Bibliography

776

(9)

Index

785

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