Preface

1 Introduction

1.1 A Brief History

1.2 Some Examples

1.3 A Chapter Summary

2 Probability

2.1 Introduction...............

2.2 Sample Spaces and the Algebra of Sets

2.3 . The Probability Function .

2.4 Conditional Probability .

2.5 Independence . . . . . . .

2.6 Combinatorics.......

2.7 Combinatorial Probability

2.8 Taking a Second Look at Statistics (Enumeration and

Monte Carlo Techniques) ................

3 Random Variableli

3.1 Introduction..................

3.2 Binomial and Hypergeometric Probabilities

3.3 Discrete Random Variables . .

3.4 Continuous Random Variables

3.5 Expected Values.

3.6 The Variance. . . . . . . . . . .

3.7 Joint Densities . . . . . . . . . .

3.8 Combining Random Variables.

3.9 Further Properties of the Mean and Variance

3.10 Order Statistics .........

3.11 Conditional Densities. . . . . . . . . . . . . .

3.12 Moment-Generating Functions ........

3.13 Taking a Second Look at Statistics (Intotpreting Means)

Appendix 3.A.1 MINIT AB Applications . . . . . . . . . . . .

4 Special Distributions

4.1 Introduction.......

4.2 The Poisson Distribution

4.3 The Normal Distribution

4.4 The Geometric Distribution

4.5 The Negative Binomial Distribution.

4.6 The Gamma Distribution

4.7 Taking a Second Look at Statistics (Monte Carlo

Simulations)

Appendix 4.A.l MINITAB Applications.

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

5 Estimation

5.1 Introduction

5.2 Estimating Parameters: The Method of Maximum Likelihood

and the Method of Moments

5.3 Interval Estimation

5.4 Properties of Estimators

5.5 Minimum-Variance Estimators: The Cramer-Rao Lower Bound . 394

5.6 Sufficient Estimators

5.7 Consistency

5.8 Bayesian Estimation

5.9 Taking a Second Look at Statistics (Revisiting the Margin of Error) . 423

Appendix 5.A.1 MINIT AB Applications

6 Hypothesis Testing

6.1 Introduction .

6.2 The Decision Rule.

6.3 Testing Binomial Data-Ho: P = Po

6.4 Type I and Type IT Errors

6.5 A Notion of Optimality: The Generalized Likelihood Ratio

6.6 Taking a Second Look at Statistics (Statistical Significance

versus "Practical" Significance)

7 The Normal Distribution

7.1 Introduction

7.2 Comparing In and J; In

7.3 Deriving the Distribution of %/

7.4 Drawing Inferences About J1

7.5 Drawing Inferences About a 2

7.6 Taking a Second Look at Statistics ("Bad" Estimators) .

Appendix 7.Al MINIT AB Applications

Appendix 7.A2 Some Distribution Results for Y and S2 . . .

Appendix 7.A3 A Proof of Theorem 7.5.2

Appendix 7.A4 A Proof that the One-Sample t Test Is a GLRT

8 Types of Data: A Brief Overview

8.1 Introduction

8.2 Classifying Data

8.3 Taking a Second Look at Statistics (Samples Are Not "Valid")

9 Two-Sample Problems

9.1 Introduction

9.2 Testing Ho: fLx = fLy-The Two-Sample t Test.

9.3 Testing Ho: a = ai-The FTest

9.4 Binomial Data: Testing Ho: px = py

9.5 Confidence Intervals for the Two-Sample Problem

9.6 Taking a Second Look at Statistics (Choosing Samples)

Appendix 9.A.l A Derivation of the Two-Sample t Test

(A Proof of Theorem 9.2.2)

Appendix 9.A.2 MINITAB Applications

10 Goodness-of-Fit Tests

10.1 Introduction

10.2 The Multinomial Distribution

10.3 Goodness-of-Fit Tests: All Parameters Known

10.4 Goodness-of-Fit Tests: Parameters Unknown

10.5 Contingency Tables

10.6 Taking a Second Look at Statistics (Outliers) .

Appendix 1O.A.l MINITAB Applications

U Regression

11.1 Introduction

11.2 The Method of Least Squares

11.3 TheLinearModel

11.4 Covariance and Correlation

11.5 The Bivariate Normal Distribution

11.6 Taking a Second Look at Statistics (How Not to Interpret the Sample

Correlation Coefficient)

Appendix 11.A.l MINITAB Applications

Appendix 11.A.2 A Proof of Theorem

12 The Analysis of Variance

12.1 Introduction

12.2 The F Test

12.3 Multiple Comparisons: Tukey's Method

12.4 Testing Subhypotheses with Contrasts

12.5 Data Transformations

12.6 Taking a Second Look at Statistics (Putting the Subject of Statistics

Together-The Contributions of Ronald A. Fisher)

Appendix 12.A.l MINITAB Applications

Appendix 12.A.2 A Proof of Theorem

Appendix 12.A.3

13 Randomized Block Designs

13.1 Introduction

13.2 The FTest for a Randomized Block Design

13.3 The Paired t Test

13.4 Taking a Second Look at Statistics (Choosing Between a Two-Sample

t Test and a Paired t Test)

Appendix 13.A.l MINITAB Applications .

14 Nonparametric Statistics

14.1 Introduction

14.2 The Sign Test

14.3 Wilcoxon Tests.

14.4 The Kruskal-Wallis Test

14.5 The Friedman Test

14.6 Testing for Randomness

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

Appendix 14.A.1 MINITAB Applications

Appendix: Statistical Tables

Answers to Selected Odd-Numbered Questions

Bibliography

Index

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## 0 有用 王特力 2008-03-19

这个学期在用，下个学期还要用...后面的作业有不少还挺难

## 0 有用 王特力 2008-03-19

这个学期在用，下个学期还要用...后面的作业有不少还挺难