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Introduction to Mathematical Statistics and Its Applications

ISBN-10: 0131867938
ISBN-13: 9780131867932
Edition: 4th 2006 (Revised)
List price: $153.33
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Description: 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  More...

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Book details

List price: $153.33
Edition: 4th
Copyright year: 2006
Publisher: Prentice Hall PTR
Publication date: 11/30/2005
Binding: Hardcover
Pages: 928
Size: 8.25" wide x 9.25" long x 1.25" tall
Weight: 3.652
Language: English

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 methods to a wide variety of real-world situations. Discusses practical problems in the application of the ideas covered in each chapter, as well as common misunderstandings or faulty approaches. Revised Minitab sections now conform to the Version 14, the latest release. For anyone interested in learning more about mathematical statistics.

A Brief History
Some Examples
A Chapter Summary
Sample Spaces and the Algebra of Sets
The Probability Function
Conditional Probability
Combinatorial Probability
Random Variables
Binomial and Hypergeometric Probabilities
Discrete Random Variables
Continuous Random Variables
Expected Values
The Variance
Joint Densities
Combining Random Variables
Further Properties of the Mean and Variance
Order Statistics
Conditional Densities
Moment Generating Functions
Odds and Ends
Special Distributions
The Poisson Distribution
The Normal Distribution
The Geometric Distribution
The Negative Binomial Distribution
The Gamma Distribution
Appendix 4.A.1: MINITAB Applications
Appendix 4.A.2: A Proof of the Central Limit Theorem
Estimating Parameters: The Method of Maximum Likelihood and the Method of Moments
Interval Estimation
Properties of Estimators
Minimum-Variance Estimators: The Cramer-Rao Lower Bound
Appendix 5.A.1: MINITAB Applications
Hypothesis Testing
The Decision Rule
Testing Binomial Data H0: p = p 0
Type I and Type II Errors
A Notion of Optimality: The Generalized Likelihood Ratio
The Normal Distribution
Comparing and . Deriving the distribution of . Drawing inferences about m
Drawing inferences about . Odds and Ends
Types of Data: A Brief Overview
Classifying Data
Two-Sample Problems
Testing H 0: mx = mY The Two-Sample t Test
Testing H0: s2x = s2Y The F Test
Binomial Data: Testing H 0: px = py
Confidence Intervals for the Two-Sample Problem
Appendix 9.A.1: A Derivation of the Two-Sample t Test (A Proof of Theorem 9.2.2.)
Appendix 9.A.2: Power Calculations for a Two-Sample t Test
Appendix 9.A.3: MINITAB Applications
Goodness-of-Fit Tests
The Multinomial Distribution
Goodness-of-Fit Tests: All Parameters Known
Goodness-of-Fit Tests: Parameters Unknown
Contingency Tables
Appendix 10.A.1: MINITAB Applications
The Method of Least Squares
The Linear Model
Covariance and Correlation
The Bivariate Normal Distribution
Appendix 11.A.1: MINITAB Applications
Appendix 11.A.2: A Proof of Theorem 11.3.3
The Analysis of Variance
The F Test
Multiple Comparisons: Tukey's Method
Testing Subhypotheses with Orthogonal Contrasts
Data Transformations
Appendix 12.A.1: MINITAB Applications
Appendix 12.A.2: A Proof of Theorem 12.2.2
Appendix 12.A.3: The Distribution of When H1 Is True
Randomized Block Designs
The F Test for a Randomized Block Design
The Paired t Test
Appendix 13.A.1: MINITAB Applications
Nonparametric Statistics
The Sign Test
The Wilcoxon Signed Rank Test
The Kruskal-Wallis Test
The Friedman Test
Appendix 14.A.1: MINITAB Applications
Appendix: Statistical Tables
Answers to Selected Odd-Numbered Questions

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