Rent 9780132546089 | Probability and Statistical Inference | Robert V. Hogg; Elliot A. Tanis @knetbooks.com

Summary Table of Contents

An accessible introduction to the mathematics of probability and statistics for students with a background in calculus. Numerous applications help to explain and motivate the concepts. This revision features a more flexible organization to better meet the needs of one or two semester courses requiring varying levels of rigor. Easier than Hogg/Craig.

List of Figures

(3)

List of Tables

(2)

Preface

... MORE

(61)

1.1 Basic Concepts

(14)

1.2 Numerical Characteristics

(7)

1.3 Exploratory Data Analysis

(10)

1.4 Graphical Comparisons of Data Sets

(9)

1.5 Time Sequences

(7)

1.6 Scatter Plots, Least Squares, and Correlation

(14)

2 Probability

(43)

2.1 Properties of Probability

(9)

2.2 Methods of Enumeration

(11)

2.3 Conditional Probability

(11)

2.4 Independent Events

(8)

2.5 Bayes' Theorem

101

(4)

3 Discrete Distributions

105

(75)

3.1 Random Variables of the Discrete Type

105

(7)

3.2 Mathematical Expectation

112

(6)

3.3 The Mean, Variance, and Standard Deviation

118

(8)

3.4 The Discrete Uniform and Hypergeometric Distributions

126

(9)

3.5 Bernoulli Trials and the Binomial Distribution

135

(12)

3.6 Geometric and Negative Binomial Distributions

147

(10)

3.7 The Poisson Distribution

157

(11)

3.8 Generating Functions

168

(12)

4 Continuous Distributions

180

(57)

4.1 Random Variables of the Continuous Type

180

(11)

4.2 The Uniform and Exponential Distributions

191

(10)

4.3 The Gamma and Chi-Square Distributions

201

(8)

4.4 The Normal Distribution

209

(13)

4.5 Distributions of Functions of a Random Variable

222

(8)

4.6 Mixed Distributions and Censoring

230

(7)

5 Sampling Distribution Theory

237

(45)

5.1 Independent Random Variables

237

(8)

5.2 Distributions of Sums of Independent Random Variables

245

(9)

5.3 Random Functions Associated with Normal Distributions

254

(8)

5.4 The Central Limit Theorem

262

(8)

5.5 Approximations for Discrete Distributions

270

(7)

5.6 Limiting Moment-Generating Functions

277

(5)

6 Estimation

282

(54)

6.1 Point Estimation

282

(12)

6.2 Confidence Intervals for Means

294

(11)

6.3 Confidence Intervals for Difference of Two Means

305

(7)

6.4 Confidence Intervals for Variances

312

(8)

6.5 Confidence Intervals for Proportions

320

(6)

6.6 Sample Size

326

7 Tests of Statistical Hypotheses

336

(78)

7.1 Tests about Proportions

336

(10)

7.2 Power and Sample Size

346

(12)

7.3 Tests about One Mean and One Variance

358

(14)

7.4 Tests of the Equality of Two Normal Distributions

372

(13)

7.5 Chi-Square Goodness-of-Fit Tests

385

(14)

7.6 Contingency Tables

399

(15)

8 Linear Models

414

(48)

8.1 Tests of the Equality of Several Means

414

(11)

8.2 Two-Factor Analysis of Variance

425

(13)

8.3 Simple Regression Problem

438

(12)

8.4 More Regression

450

(12)

9 Quality Improvement Through Statistical Methods

462

(31)

9.1 Shewhart Control Charts

462

(13)

9.2 General Factorial and 2k Factorial Designs

475

(8)

9.3 More on Design of Experiments

483

(5)

9.4 Quality Improvement by Understanding Variability

488

(5)

10 Nonparametric Methods

493

(59)

10.1 Order Statistics

493

(11)

10.2 Confidence Intervals for Percentiles

504

(8)

10.3 Binomial Tests for Percentiles

512

(7)

10.4 The Wilcoxon Test

519

(8)

10.5 Two-Sample Distribution-Free Tests

527

(9)

10.6 Run Test and Test for Randomness

536

(8)

10.7 Kolmogorov-Smirnov Goodness-of-Fit Test

544

(8)

11 Multivariate Distributions

552

(53)

11.1 Multivariate Distributions

552

(13)

11.2 The Correlation Coefficient

565

(7)

11.3 Conditional Distributions

572

(11)

11.4 The Bivariate Normal Distribution

583

(7)

11.5 Correlation Analysis

590

(6)

11.6 Transformations of Random Variables

596

(9)

12 Theory of Statistical Inference

605

(36)

12.1 Sufficient Statistics

605

(4)

12.2 Bayesian Estimation

609

(6)

12.3 Asymptotic Distributions of Maximum Likelihood Estimators

615

(5)

12.4 Chebyshev's Inequality and Convergence in Probability

620

(5)

12.5 Best Critical Regions

625

(8)

12.6 Likelihood Ratio Tests

633

(8)

A REVIEW OF SELECTED MATHEMATICAL TECHNIQUES

641

(1)

A.1 Algebra of Sets

641

(4)

A.2 Mathematical Tools for the Hypergeometric Distribution

645

(3)

A.3 Limits

648

(2)

A.4 Infinite Series

650

(4)

A.5 Integration

654

(2)

A.6 Multivariate Calculus

656

(5)

B REFERENCES

661

(2)

C TABLES

663

(1)

Table I Binomial Coefficients

664

(1)

Table II The Binomial Distribution

665

(7)

Table III The Poisson Distribution

672

(3)

Table IV The Chi-Square Distribution

675

(1)

Table Va The Standard Normal Distribution Function

676

(1)

Table Vb The Standard Normal Right Tail Probabilities

677

(1)

Table VI The t Distribution

678

(1)

Table VII The F Distribution

679

(5)

Table VIII The Kolmogrov-Smirnov Acceptance Limits

684

(1)

Table IX Random Numbers on the Interval (0, 1)

685

(1)

Table X Divisors for the Confidence Interval for XXX of Minimum Length

686

(1)

Table XI Distribution Function of the Correlation Coefficient R

687

(1)

Answers to Odd-Numbered Exercises

688

(29)

Index

717

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Probability and Statistical Inference

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