Introduction to Mathematical Statistics and Its Applications, An,9780139223037

Introduction to Mathematical Statistics and Its Applications, An

by ;
Edition: 3rd
ISBN13: 9780139223037
ISBN10: 0139223037
Format: Hardcover
Pub. Date: 2001-01-01
Publisher(s): Pearson College Div
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Summary

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. For anyone needing to develop proficiency with Mathematical Statistics.

Table of Contents

Preface xi
Introduction
1(19)
A Brief History
2(9)
Some Examples
11(7)
A Chapter Summary
18(2)
Probability
20(99)
Introduction
21(1)
Sample Spaces and the Algebra of Sets
21(8)
The Probability Function
29(7)
Discrete Probability Functions
36(6)
Continuous Probability Functions
42(9)
Conditional Probability
51(19)
Independence
70(9)
Repeated Independent Trials
79(7)
Combinatorics
86(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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