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手植记:最稀缺仅有的4种原生态食材

手植记:最稀缺仅有的4种原生态食材

  最稀缺仅有的4种原生态食材

  《舌尖上的中国2》热播,引得饕餮客们食指大动的同时,也引发人们对“原生态”食物的热捧——土榨菜籽油、深山野蜂蜜制成的酥油蜂蜜……各种带着浓浓乡味的食材更获赞“最健康”,甚至直接带旺了各类产地直销的“原生态”食品的网购潮。

  在淘宝上有一家店铺叫:手植记。他们发起了一个全国探寻原生态食材的活动:手植之旅,为生活寻找原生态食材。作为美食编辑的我,通过官方的400电话联系到了手植之旅的负责人.通过和负责人的沟通,彻彻底底了解了一下“原生态”。如何定义原生态,让我们通过以下几点来看看:

  用地理位置产物来定义的“原生态”几乎没有原生态之说

  特有的某地理位置产物,地处长江边,地形和水位,降水和日照,用这样的关键词包装出太多的“原生态”食材。其实在理论上讲,确实是有“地理位置产物”因特殊的土壤环境出土的食材其味道就是最棒的。但往往追根到底,确发现那些特殊的环境产量是少之又少。过度的商业包装,任何地方的食材都被过度到这个“地理位置产物”的标签上。各大超市,各大网站,加上我们庞大的生活消费群体,那区区几亩田地根本没有这么大的产量。

  用特产特有来定义的“原生态”几乎断绝

  我们总是习惯到达过某个地方,而采购“特产”带给朋友送去最真挚的祝福。送健康,是我们注重“养生”这个群体运动的产物。食材被加以健康又被过多的“特产”包装。手植之旅走过的地方,挨家有户遍寻问其“特产”,有的略有所知,有的根本不知道他们当地仅有此“神仙之食”。通过翻书和网络搜索,某些“特产”确实有记载,但随着人民生活水平的提高,几乎已经不再生产或者种植一些不能保证经济收入的“特产”食物。

  包装“农民”形象就是原生态食材之说支撑度不够

  一身灰色的中山装加一除草的锄头,市场上充斥着太多用“农民”形象包装而成的纯天然,健康等的“原生态”食材。通过手植之旅的每一站的实地考察,那些本土确实用“农家施肥”而保持几乎近似野生生长的庄稼,根本就很难进入市场,只能够满足当地农民3口之家的食用。大面积的田地,全都为了生活改种产量大利润高的农作物。经济的快速发展,“农民”的生活也已经节奏加快,社会改变着我们,社会侵蚀了那本有的“原生态”。

  原生态食材依靠自然生长,几乎近似野生生长。实在是遇到恶劣的干旱天气或是虫灾,这个时候适当的人为参与是为了保证其产量。在整个种植过程中,无法过多的参与其作物生长,只能让他适应环境而生存的食材,其实已经很少,和动物的灭绝一样,食材也因稀缺频临灭绝。

  陈集西施种子山药即将灭绝的真原生态食材

  种植西施种子山药的土地需要在5年前开始培育,也就是说种过西施种子山药的土地需要空5年以上不能种植其他任何农作物,土地已经无营养,只有用5年的时间培育土地,而后再第六年种植西施种子山药或其他农作物。因特殊的无性繁殖,不结豆,只能用根茎繁殖,所以种植面积难以扩大,让其珍贵无比。

  对土地的伤害要5年恢复,西施种子山药整个菏泽不足百亩,频临灭绝。

  沂蒙椿树沟松菇纯天然的食材

  椿树沟一个原始的村落,上山进村需要延山路驱车2个小时,然后再步行1个小时。满山的松树环保着一个小村落,十几户人家。因为没有太多的商业用地,所以采取野生生长的松菇成了山里村民最基本的经济来源。

  松菇,除具备一般蘑菇生长条件外,还必须与松树生长在一起,与松树根共生,其生长环境为海拔700到500米的阴坡或半阴坡的松树林中。产菇的林龄一般不低于50年。

  莒县库山丹参近似野生的食材之一

  库山的特殊山区环境,造就了近似野生生长的中药材丹参。

  苍山牛蒡和山药一样1米深土地下的食材

  东洋参,学名牛蒡,又名东洋参,东洋牛鞭菜等。一千多年前日本从中国引进并改良成食物,在日本占据台湾时曾在台南要求当地农民大量种植,主要原因是台南有曾文溪畔松沙土质、北回归线气候加上有名阿里山延脉造就其当地牛蒡得天独厚的珍贵性,台湾已作为蔬菜食用多年,有牛蒡发祥地之称,中国大陆则以山东临沂苍山庄坞为最。

  手植记的负责人最后给我说:真正的原生态食材是少之又少,农耕不易,食材珍惜,请尊重这些即将消失的原生态食材。

手植记
我们快乐&精神食粮
为生活寻找原生态食材

AN INTRODUCTION TO MATHEMATICAL STATISTICS AND ITS APPLICATIONS

AN INTRODUCTION TO
MATHEMATICAL STATISTICS
AND ITS APPLICATIONS
Fifth Edition
Richard J. Larsen
Vanderbilt University
Morris L. Marx
University of West Flori

Table of Contents
Preface viii
1 Introduction 1
1.1 An Overview 1
1.2 Some Examples 2
1.3 A Brief History 7
1.4 A Chapter Summary 14
2 Probability 16
2.1 Introduction 16
2.2 Sample Spaces and the Algebra of Sets 18
2.3 The Probability Function 27
2.4 Conditional Probability 32
2.5 Independence 53
2.6 Combinatorics 67
2.7 Combinatorial Probability 90
2.8 Taking a Second Look at Statistics (Monte Carlo Techniques) 99
3 Random Variables 102
3.1 Introduction 102
3.2 Binomial and Hypergeometric Probabilities 103
3.3 Discrete Random Variables 118
3.4 Continuous Random Variables 129
3.5 Expected Values 139
3.6 The Variance 155
3.7 Joint Densities 162
3.8 Transforming and Combining Random Variables 176
3.9 Further Properties of the Mean and Variance 183
3.10 Order Statistics 193
3.11 Conditional Densities 200
3.12 Moment-Generating Functions 207
3.13 Taking a Second Look at Statistics (Interpreting Means) 216
Appendix 3.A.1 Minitab Applications 218
iii

4 Special Distributions 221
4.1 Introduction 221
4.2 The Poisson Distribution 222
4.3 The Normal Distribution 239
4.4 The Geometric Distribution 260
4.5 The Negative Binomial Distribution 262
4.6 The Gamma Distribution 270
4.7 Taking a Second Look at Statistics (Monte Carlo
Simulations) 274
Appendix 4.A.1 Minitab Applications 278
Appendix 4.A.2 A Proof of the Central Limit Theorem 280
5 Estimation 281
5.1 Introduction 281
5.2 Estimating Parameters: The Method of Maximum Likelihood and
the Method of Moments 284
5.3 Interval Estimation 297
5.4 Properties of Estimators 312
5.5 Minimum-Variance Estimators: The Cramér-Rao Lower
Bound 320
5.6 Sufficient Estimators 323
5.7 Consistency 330
5.8 Bayesian Estimation 333
5.9 Taking a Second Look at Statistics (Beyond Classical
Estimation) 345
Appendix 5.A.1 Minitab Applications 346
6 Hypothesis Testing 350
6.1 Introduction 350
6.2 The Decision Rule 351
6.3 Testing Binomial Data—H0: p = po 361
6.4 Type I and Type II Errors 366
6.5 A Notion of Optimality: The Generalized Likelihood Ratio 379
6.6 Taking a Second Look at Statistics (Statistical Significance versus
“Practical” Significance) 382

7 Inferences Based on the Normal
Distribution 385
7.1 Introduction 385
7.2 Comparing Y?μ
σ/

n and Y?μ
S/

n
386
7.3 Deriving the Distribution of Y?μ
S/

n
388
7.4 Drawing Inferences About μ 394
7.5 Drawing Inferences About σ2 410
7.6 Taking a Second Look at Statistics (Type II Error) 418
Appendix 7.A.1 Minitab Applications 421
Appendix 7.A.2 Some Distribution Results for Y and S2 423
Appendix 7.A.3 A Proof that the One-Sample t Test is a GLRT 425
Appendix 7.A.4 A Proof of Theorem 7.5.2 427
8 Types of Data: A Brief Overview 430
8.1 Introduction 430
8.2 Classifying Data 435
8.3 Taking a Second Look at Statistics (Samples Are Not
“Valid”!) 455
9 Two-Sample Inferences 457
9.1 Introduction 457
9.2 Testing H0: μX =μY 458
9.3 Testing H0: σ2
X
=σ2
Y—The F Test 471
9.4 Binomial Data: Testing H0: pX = pY 476
9.5 Confidence Intervals for the Two-Sample Problem 481
9.6 Taking a Second Look at Statistics (Choosing Samples) 487
Appendix 9.A.1 A Derivation of the Two-Sample t Test (A Proof of
Theorem 9.2.2) 488
Appendix 9.A.2 Minitab Applications 491
10 Goodness-of-Fit Tests 493
10.1 Introduction 493
10.2 The Multinomial Distribution 494
10.3 Goodness-of-Fit Tests: All Parameters Known 499
10.4 Goodness-of-Fit Tests: Parameters Unknown 509
10.5 Contingency Tables 519

10.6 Taking a Second Look at Statistics (Outliers) 529
Appendix 10.A.1 Minitab Applications 531
11 Regression 532
11.1 Introduction 532
11.2 The Method of Least Squares 533
11.3 The Linear Model 555
11.4 Covariance and Correlation 575
11.5 The Bivariate Normal Distribution 582
11.6 Taking a Second Look at Statistics (How Not to Interpret
the Sample Correlation Coefficient) 589
Appendix 11.A.1 Minitab Applications 590
Appendix 11.A.2 A Proof of Theorem 11.3.3 592
12 The Analysis of Variance 595
12.1 Introduction 595
12.2 The F Test 597
12.3 Multiple Comparisons: Tukey’s Method 608
12.4 Testing Subhypotheses with Contrasts 611
12.5 Data Transformations 617
12.6 Taking a Second Look at Statistics (Putting the Subject of
Statistics Together—The Contributions of Ronald A. Fisher) 619
Appendix 12.A.1 Minitab Applications 621
Appendix 12.A.2 A Proof of Theorem 12.2.2 624
Appendix 12.A.3 The Distribution of SSTR/(k–1)
SSE/(n–k) When H1 is True 624
13 Randomized Block Designs 629
13.1 Introduction 629
13.2 The F Test for a Randomized Block Design 630
13.3 The Paired t Test 642
13.4 Taking a Second Look at Statistics (Choosing between a
Two-Sample t Test and a Paired t Test) 649
Appendix 13.A.1 Minitab Applications 653
14 Nonparametric Statistics 655
14.1 Introduction 656
14.2 The Sign Test 657

14.3 Wilcoxon Tests 662
14.4 The Kruskal-Wallis Test 677
14.5 The Friedman Test 682
14.6 Testing for Randomness 684
14.7 Taking a Second Look at Statistics (Comparing Parametric
and Nonparametric Procedures) 689
Appendix 14.A.1 Minitab Applications 693
Appendix: Statistical Tables 696
Answers to Selected Odd-Numbered Questions 723
Bibliography 745
Index 753

The first edition of this text was published in 1981. Each subsequent revision since
then has undergone more than a few changes. Topics have been added, computer
software and simulations introduced, and examples redone. What has not
changed over the years is our pedagogical focus. As the title indicates, this book
is an introduction to mathematical statistics and its applications. Those last three
words are not an afterthought. We continue to believe that mathematical statistics
is best learned and most effectively motivated when presented against a backdrop
of real-world examples and all the issues that those examples necessarily
raise.
We recognize that college students today have more mathematics courses to
choose from than ever before because of the new specialties and interdisciplinary
areas that continue to emerge. For students wanting a broad educational experience,
an introduction to a given topic may be all that their schedules can reasonably
accommodate. Our response to that reality has been to ensure that each edition of
this text provides a more comprehensive and more usable treatment of statistics
than did its predecessors.
Traditionally, the focus of mathematical statistics has been fairly narrow—the
subject’s objective has been to provide the theoretical foundation for all of the various
procedures that are used for describing and analyzing data. What it has not
spoken to at much length are the important questions of which procedure to use
in a given situation, and why. But those are precisely the concerns that every user
of statistics must inevitably confront. To that end, adding features that can create
a path from the theory of statistics to its practice has become an increasingly high
priority.
New to This Edition
? Beginning with the third edition, Chapter 8, titled “Data Models,” was added.
It discussed some of the basic principles of experimental design, as well as some
guidelines for knowing how to begin a statistical analysis. In this fifth edition, the
Data Models (“Types of Data: A Brief Overview”) chapter has been substantially
rewritten to make its main points more accessible.
? Beginning with the fourth edition, the end of each chapter except the first featured
a section titled “Taking a Second Look at Statistics.” Many of these sections
describe the ways that statistical terminology is often misinterpreted in what we
see, hear, and read in our modern media. Continuing in this vein of interpretation,
we have added in this fifth edition comments called “About the Data.”
These sections are scattered throughout the text and are intended to encourage
the reader to think critically about a data set’s assumptions, interpretations, and
implications.
? Many examples and case studies have been updated, while some have been
deleted and others added.
? Section 3.8, “Transforming and Combining Random Variables,” has been
rewritten.
viii

? Section 3.9, “Further Properties of the Mean and Variance,” now includes a discussion
of covariances so that sums of random variables can be dealt with in more
generality.
? Chapter 5, “Estimation,” now has an introduction to bootstrapping.
? Chapter 7, “Inferences Based on the Normal Distribution,” has new material on
the noncentral t distribution and its role in calculating Type II error probabilities.
? Chapter 9, “Two-Sample Inferences,” has a derivation of Welch’s approximation
for testing the differences of two means in the case of unequal
variances.
We hope that the changes in this edition will not undo the best features of the
first four. What made the task of creating the fifth edition an enjoyable experience
was the nature of the subject itself and the way that it can be beautifully elegant and
down-to-earth practical, all at the same time. Ultimately, our goal is to share with
the reader at least some small measure of the affection we feel for mathematical
statistics and its applications.
Supplements
Instructor’s Solutions Manual. This resource contains worked-out solutions to
all text exercises and is available for download from the Pearson Education
Instructor Resource Center.
Student Solutions Manual ISBN-10: 0-321-69402-3; ISBN-13: 978-0-321-
69402-7. Featuring complete solutions to selected exercises, this is a great tool
for students as they study and work through the problem material.
Acknowledgments
We would like to thank the following reviewers for their detailed and valuable
comments, criticisms, and suggestions:
Dr. Abera Abay, Rowan University
Kyle Siegrist, University of Alabama in Huntsville
Ditlev Monrad, University of Illinois at Urbana-Champaign
Vidhu S. Prasad, University of Massachusetts, Lowell
Wen-Qing Xu, California State University, Long Beach
Katherine St. Clair, Colby College
Yimin Xiao, Michigan State University
Nicolas Christou, University of California, Los Angeles
Daming Xu, University of Oregon
Maria Rizzo, Ohio University
Dimitris Politis, University of California at San Diego
Finally, we convey our gratitude and appreciation to Pearson Arts & Sciences
Associate Editor for Statistics Christina Lepre; Acquisitions Editor Christopher
Cummings; and Senior Production Project Manager Peggy McMahon, as well as

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