Introduction to Mathematical Statistics and Its Applications, An

by Larsen, Richard J.; Marx, Morris L.

• ISBN13: 9780139223037
• ISBN10: 0139223037
• Edition: 3rd
• Format: Hardcover
• Copyright: 2001-01-01
• Publisher: Pearson College Div

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