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Mathematical Statistics and Data Analysis (with CD Data Sets),9780534399429
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Mathematical Statistics and Data Analysis (with CD Data Sets)

by
Edition:
3rd
ISBN13:

9780534399429

ISBN10:
0534399428
Format:
Hardcover
Pub. Date:
4/28/2006
Publisher(s):
Cengage Learning
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This is the 3rd edition with a publication date of 4/28/2006.
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Summary

This is the first text in a generation to re-examine the purpose of the mathematical statistics course. The book's approach interweaves traditional topics with data analysis and reflects the use of the computer with close ties to the practice of statistics. The author stresses analysis of data, examines real problems with real data, and motivates the theory. The book's descriptive statistics, graphical displays, and realistic applications stand in strong contrast to traditional texts that are set in abstract settings.

Table of Contents

Preface xi
Probability
1(34)
Introduction
1(1)
Sample Spaces
2(2)
Probability Measures
4(2)
Computing Probabilities: Counting Methods
6(10)
The Multiplication Principle
7(2)
Permutations and Combinations
9(7)
Conditional Probability
16(7)
Independence
23(3)
Concluding Remarks
26(1)
Problems
26(9)
Random Variables
35(36)
Discrete Random Variables
35(12)
Bernoulli Random Variables
37(1)
The Binomial Distribution
38(2)
The Geometric and Negative Binomial Distributions
40(2)
The Hypergeometric Distribution
42(1)
The Poisson Distribution
42(5)
Continuous Random Variables
47(11)
The Exponential Density
50(3)
The Gamma Density
53(1)
The Normal Distribution
54(4)
The Beta Density
58(1)
Functions of a Random Variable
58(6)
Concluding Remarks
64(1)
Problems
64(7)
Joint Distributions
71(45)
Introduction
71(1)
Discrete Random Variables
72(3)
Continuous Random Variables
75(9)
Independent Random Variables
84(3)
Conditional Distributions
87(9)
The Discrete Case
87(1)
The Continuous Case
88(8)
Functions of Jointly Distributed Random Variables
96(8)
Sums and Quotients
96(3)
The General Case
99(5)
Extrema and Order Statistics
104(3)
Problems
107(9)
Expected Values
116(61)
The Expected Value of a Random Variable
116(14)
Expectations of Functions of Random Variables
121(3)
Expectations of Linear Combinations of Random Variables
124(6)
Variance and Standard Deviation
130(8)
A Model for Measurement Error
135(3)
Covariance and Correlation
138(9)
Conditional Expectation and Prediction
147(8)
Definitions and Examples
147(5)
Prediction
152(3)
The Moment-Generating Function
155(6)
Approximate Methods
161(5)
Problems
166(11)
Limit Theorems
177(15)
Introduction
177(1)
The Law of Large Numbers
177(4)
Convergence in Distribution and the Central Limit Theorem
181(7)
Problems
188(4)
Distributions Derived from the Normal Distribution
192(7)
Introduction
192(1)
Χ2, t, and F Distributions
192(3)
The Sample Mean and the Sample Variance
195(3)
Problems
198(1)
Survey Sampling
199(56)
Introduction
199(1)
Population Parameters
200(2)
Simple Random Sampling
202(18)
The Expectation and Variance of the Sample Mean
203(7)
Estimation of the Population Variance
210(4)
The Normal Approximation to the Sampling Distribution of X
214(6)
Estimation of a Ratio
220(7)
Stratified Random Sampling
227(11)
Introduction and Notation
227(1)
Properties of Stratified Estimates
228(4)
Methods of Allocation
232(6)
Concluding Remarks
238(1)
Problems
239(16)
Estimation of Parameters and Fitting of Probability Distributions
255(74)
Introduction
255(1)
Fitting the Poisson Distribution to Emissions of Alpha Particles
255(2)
Parameter Estimation
257(3)
The Method of Moments
260(7)
The Method of Maximum Likelihood
267(18)
Maximum Likelihood Estimates of Multinomial Cell Probabilities
272(2)
Large Sample Theory for Maximum Likelihood Estimates
274(5)
Confidence Intervals from Maximum Likelihood Estimates
279(6)
The Bayesian Approach to Parameter Estimation
285(13)
Further Remarks on Priors
294(2)
Large Sample Normal Approximation to the Posterior
296(1)
Computational Aspects
297(1)
Efficiency and the Cramer-Rao Lower Bound
298(7)
An Example: The Negative Binomial Distribution
302(3)
Sufficiency
305(6)
A Factorization Theorem
306(4)
The Rao-Blackwell Theorem
310(1)
Concluding Remarks
311(1)
Problems
312(17)
Testing Hypotheses and Assessing Goodness of Fit
329(48)
Introduction
329(2)
The Neyman-Pearson Paradigm
331(6)
Specification of the Significance Level and the Concept of a p-value
334(1)
The Null Hypothesis
335(1)
Uniformly Most Powerful Tests
336(1)
The Duality of Confidence Intervals and Hypothesis Tests
337(2)
Generalized Likelihood Ratio Tests
339(2)
Likelihood Ratio Tests for the Multinomial Distribution
341(6)
The Poisson Dispersion Test
347(2)
Hanging Rootograms
349(3)
Probability Plots
352(6)
Tests for Normality
358(3)
Concluding Remarks
361(1)
Problems
362(15)
Summarizing Data
377(43)
Introduction
377(1)
Methods Based on the Cumulative Distribution Function
378(11)
The Empirical Cumulative Distribution Function
378(2)
The Survival Function
380(5)
Quantile-Quantile Plots
385(4)
Histograms, Density Curves, and Stem-and-Leaf Plots
389(3)
Measures of Location
392(9)
The Arithmetic Mean
393(2)
The Median
395(2)
The Trimmed Mean
397(1)
M Estimates
397(1)
Comparison of Location Estimates
398(1)
Estimating Variability of Location Estimates by the Bootstrap
399(2)
Measures of Dispersion
401(1)
Boxplots
402(2)
Exploring Relationships with Scatterplots
404(3)
Concluding Remarks
407(1)
Problems
408(12)
Comparing Two Samples
420(57)
Introduction
420(1)
Comparing Two Independent Samples
421(23)
Methods Based on the Normal Distribution
421(12)
Power
433(2)
A Nonparametric Method--The Mann-Whitney Test
435(8)
Bayesian Approach
443(1)
Comparing Paired Samples
444(8)
Methods Based on the Normal Distribution
446(2)
A Nonparametric Method--The Signed Rank Test
448(2)
An Example--Measuring Mercury Levels in Fish
450(2)
Experimental Design
452(7)
Mammary Artery Ligation
452(1)
The Placebo Effect
453(1)
The Lanarkshire Milk Experiment
453(1)
The Portacaval Shunt
454(1)
FD&C Red No. 40
455(1)
Further Remarks on Randomization
456(1)
Observational Studies, Confounding, and Bias in Graduate Admissions
457(1)
Fishing Expeditions
458(1)
Concluding Remarks
459(1)
Problems
459(18)
The Analysis of Variance
477(37)
Introduction
477(1)
The One-Way Layout
477(12)
Normal Theory; the F Test
478(7)
The Problem of Multiple Comparisons
485(3)
A Nonparametric Method--The Kruskal-Wallis Test
488(1)
The Two-Way Layout
489(15)
Additive Parametrization
489(3)
Normal Theory for the Two-Way Layout
492(8)
Randomized Block Designs
500(3)
A Nonparametric Method--Friedman's Test
503(1)
Concluding Remarks
504(1)
Problems
505(9)
The Analysis of Categorical Data
514(28)
Introduction
514(1)
Fisher's Exact Test
514(2)
The Chi-Square Test of Homogeneity
516(4)
The Chi-Square Test of Independence
520(3)
Matched-Pairs Designs
523(3)
Odds Ratios
526(4)
Concluding Remarks
530(1)
Problems
530(12)
Linear Least Squares
542
Introduction
542(5)
Simple Linear Regression
547(17)
Statistical Properties of the Estimated Slope and Intercept
547(3)
Assessing the Fit
550(10)
Correlation and Regression
560(4)
The Matrix Approach to Linear Least Squares
564(3)
Statistical Properties of Least Squares Estimates
567(13)
Vector-Valued Random Variables
567(6)
Mean and Covariance of Least Squares Estimates
573(2)
Estimation of σ2
575(1)
Residuals and Standardized Residuals
576(1)
Inference about β
577(3)
Multiple Linear Regression---An Example
580(5)
Conditional Inference, Unconditional Inference, and the Bootstrap
585(2)
Local Linear Smoothing
587(4)
Concluding Remarks
591(1)
Problems
591
Appendix A Common Distributions 1(3)
Appendix B Tables 4(21)
Bibliography 25(7)
Answers to Selected Problems 32(16)
Author Index 48(3)
Applications Index 51(3)
Subject Index 54


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