statistics-1bykeller
albiononline statistics analysis
albiononline statistics analysisAnalyzing Albion Online statistics can provide valuable insights into various aspects of the game, such as player population, economy, PvP performance, and guild activities. Here are a few key areas that can be analyzed:1. Player Population: One can analyze the number of active players, their distribution across different zones, factions, or timezones. This information can help assess the popularity of the game and identify areas where player engagement may be lacking or thriving.2. Economy: Analyzing the game's economy can involve studying auction house transactions, prices of items, and analyzing supply and demand patterns. This can help determine which types of resources are in high demand, which can be valuable information for players looking to make a profit.3. PvP Performance: By analyzing player-versus-player combat data, one can determine the effectiveness of different types of builds, weapons, or armor sets. This can help players optimize their combat strategies, as well as provide insights into any imbalances in the game's combat mechanics that may need addressing.4. Guild Activities: Analyzing guild-related statistics can provide useful insights into the dynamics of player alliances and guilds. This can include tracking alliances' territorial control, guild member activities, and participation in large-scale battles or guild vs. guild events.5. PvE Progression: Analyzing player progression data, such as dungeon completion rates or boss kills, can help identify any content that may be too difficult or too easy for players. Developers can then adjust game difficulty or balance accordingly. To perform these analyses, data can be collected from in-game logs, API (Application Programming Interface) endpoints, or using third-party tools that track and provide game data. Analyzing Albion Online statistics can help players optimize their gameplay, aid developers in improving the game, and provide researchers with insights into player behavior in virtual worlds.。
SPSS学习笔记
SPSS学习笔记描述样本数据一般的，一组数据拿出来，需要先有一个整体认识。
除了我们平时最常用的集中趋势外，还需要一些离散趋势的数据。
这方面EXCEL就能一次性的给全了数据，但对于SPSS，就需要用多个工具了，感觉上表格方面不如EXCEL好用。
个人感觉，通过描述需要了解整体数据的集中趋势和离散趋势，再借用各种图观察数据的分布形态。
对于SPSS提供的OLAP cubes（在线分析处理表），Case Summary（观察值摘要分析表），Descriptives （描述统计）不太常用，反喜欢用Frequencies（频率分析），Basic Table（基本报表），Crosstabs（列联表）这三个，另外再配合其它图来观察。
这个可以根据个人喜好来选择。
一．使用频率分析（Frequencies）观察数值的分布。
频率分布图与分析数据结合起来，可以更清楚的看到数据分布的整体情况。
以自带文件Trends chapter 13.sav为例，选择Analyze->Descriptive Statistics->Frequencies，把hstarts选入Variables，取消在Display Frequency table前的勾，在Chart里面histogram，在Statistics选项中如图1图1分别选好均数(Mean)，中位数(Median)，众数(Mode)，总数(Sum)，标准差(Std. deviation)，方差(Variance)，范围(range)，最小值(Minimum)，最大值(Maximum)，偏度系数(Skewness)，峰度系数(Kutosis)，按Continue返回，再按OK，出现结果如图2图2表中，中位数与平均数接近，与众数相差不大，分布良好。
标准差大，即数据间的变化差异还还小。
峰度和偏度都接近0，则数据基本接近于正态分布。
下面图3的频率分布图就更直观的观察到这样的情况图3二．采用各种图直观观察数据分布情况，如采用柱型图观察归类的比例等。
ergm.count包说明书
Package‘ergm.count’May24,2022Version4.1.1Date2022-05-24Title Fit,Simulate and Diagnose Exponential-Family Models for Networks with Count Edges Depends ergm(>=4.2.1),network(>=1.15)Imports mon(>=4.2.0)LinkingTo ergmDescription A set of extensions for the'ergm'package to fit weighted net-works whose edge weights are counts.See Krivitsky(2012)<doi:10.1214/12-EJS696>and Kriv-itsky,Hunter,Morris,and Klumb(2021)<arXiv:2106.04997>.License GPL-3+file LICENSEURL https://BugReports https:///statnet/ergm.count/issuesSuggests covr,knitr,rmarkdown,testthat(>=3.0.0)VignetteBuilder rmarkdown,knitrRoxygenNote7.2.0Roxygen list(markdown=TRUE)Encoding UTF-8Config/testthat/parallel trueConfig/testthat/edition3R topics documented:ergm.count-package (2)Binomial-ergmReference (3)CMB-ergmTerm (4)CMP-ergmTerm (4)12ergm.count-package Disc-ergmProposal (5)DiscTNT-ergmProposal (5)Geometric-ergmReference (6)Poisson-ergmReference (6)zach (7)ZIPoisson-ergmProposal (9)Index10ergm.count-package Fit,Simulate and Diagnose Exponential-Family Models for Networkswith Count EdgesDescriptionergm.count is a set of extensions to package ergm to fit and simulate from exponential-family random graph models for networks whose edge weights are counts.For a list of functions type help(package='ergm')and help(package='ergm.count')DetailsMainly,it implements Poisson,binomial,geometric,and discrete uniform dyadwise reference mea-sures for valued ERGMs(documented here in ergmReference),and provides some count-specific change statistics(documented in ergmTerm).For a complete list of the functions,use library(help="ergm")and library(help="ergm.count") or read the rest of the manual.When publishing results obtained using this package,please cite the original authors as described in citation(package="ergm.count").All programs derived from this package must cite it.This package contains functions specific to using ergm to model networks whose dyad values are counts.Examples include counts of conversations,messages,and other interactions.In particular,this package implements the Poisson,geometric,binomial,and discrete uniform refer-ence measures(documented in ergmReference for use by ergm and simulate.ergm)to fit models from this family,as well as statistics specific to modeling counts,such as the CMP for the Conway-Maxwell-Poisson Distribution.For detailed information on how to download and install the software,go to the Statnet project website:https://.A tutorial,support newsgroup,references and links to further resources are provided there.Known issuesParameter space constraints:Poisson-and geometric-reference ERGMs have an unbouded sample space.This means that the parameter space may be constrained in complex ways that depend on the terms used in the model.At this time ergm has no way to detect when a parameter configuration had strayed outside of the parameter space,but it may be noticeable on a runtime trace plot(activated viaBinomial-ergmReference 3MCMC.runtime.traceplot control parameter),when the simulated values keep climbing up-wards.(See Krivitsky (2012)for a further discussion.)A possible remedy if this appears to occur is to try lowering the control parameter MCMLE.steplength .Author(s)Pavel N.Krivitsky <*****************>ReferencesHandcock MS,Hunter DR,Butts CT,Goodreau SG,Krivitsky PN and Morris M (2012).Fit,Simulate and Diagnose Exponential-Family Models for Networks .Version 3.1.Project home page at <URL:https://>,<URL:/package=ergm>.Krivitsky PN (2012).Exponential-Family Random Graph Models for Valued Networks.Electronic Journal of Statistics ,2012,6,1100-1128.doi:10.1214/12EJS696Shmueli G,Minka TP,Kadane JB,Borle S,and Boatwright P (2005).A Useful Distribution for Fitting Discrete Data:Revival of the Conway–Maxwell–Poisson Distribution.Journal of the Royal Statistical Society:Series C ,54(1):127-142.See AlsoergmTerm ,ergmReferenceBinomial-ergmReferenceBinomial-reference ERGMDescriptionSpecifies each dyad’s baselinedistribution to be binomial with trials trials and success probability of 0.5:h (y )= i,j trials y i,j .Using valued ERGM terms that are "generalized"from their binary counterparts,with form "sum"(see previous link for the list)produces logistic age#Binomial(trials)Argumentstrails model parameterSee AlsoergmReference for index of reference distributions currently visible to the package.4CMP-ergmTerm CMB-ergmTerm Conway-Maxwell-Binomial DistributionDescriptionIf couple==TRUE,this term adds one statistic to the model,of the formi,jlog(y i,j!)+log(t−y i,j!).This turns a Binomial-or a discrete-uniform-reference ERGM into a Conway-Maxwell-Binomial-reference ERGM,allowing it to represent a broad range of disperson values.In particular, combined with a Binomial-reference ERGM,a negative coefficient on this term induces underdis-persion and a positive coefficient induces overdispersion.If coupled==FALSE the two summands above are added as their own statistic(each with its own free parameter).Usage#valued:CMB(trials,coupled=TRUE)Argumentstrails model parametercoupled logicalCMP-ergmTerm Conway-Maxwell-Poisson DistributionDescriptionThis term adds one statistic to the model,of the formi,jlog(y i,j!).This turns a Poisson-or ageometric-reference ERGM into a Conway-Maxwell-Poisson-reference ERGM,allowing it to rep-resent a broad range of disperson values.In particular,combined with a Poisson-reference ERGM,a negative coefficient on this term induces underdispersion and a positive coefficient induces overdis-persion.(This behavior is different from3.1.1,when the negation of this value was used.)Usage#valued:CMPDetailsNote that its current implementation may not perform well if the data are overdispersed relative to geometric.Disc-ergmProposal5 Disc-ergmProposal Sampling for some discrete-reference ERGMsDescriptionThis proposal implements Poisson-ergmReference,Geometric-ergmReference,Binomial-ergmReference, and DiscUnif-ergmReference with arbitrary dyad level constraints.DetailsThis proposal is not referenced in the lookup table.See AlsoDiscTNT-ergmProposalDiscTNT-ergmProposal TNT sampling for some discrete-reference ERGMsDescriptionThis proposal implements Poisson-ergmReference,Geometric-ergmReference,Binomial-ergmReference, and DiscUnif-ergmReference when the range of values includes0,falling back to Disc-ergmProposal otherwise,all with arbitrary dyad-level constraints.DetailsThis proposal is not referenced in the lookup table.See AlsoTNT-ergmProposal6Poisson-ergmReference Geometric-ergmReferenceGeometric-reference ERGMDescriptionSpecifies each dyad’s baseline distribution to be uniform on the natural numbers(and0):h(y)=1 .In itself,this"distribution"is improper,but in the presence of sum,a geometric distribution is ing CMP(in addition to sum)induces a Conway-Maxwell-Poisson distribution that is geometric when its coefficient is0and Poisson when its coefficient is−1.Usage#GeometricSee AlsoergmReference for index of reference distributions currently visible to the package.Poisson-ergmReference Poisson-reference ERGMDescriptionSpecifies each dyad’s baseline distribution to be Poisson with mean1:h(y)=i,j1/y i,j!,withthe support of y i,j being natural numbers(and0).Using valued ERGM terms that are"generalized" from their binary counterparts,with form"sum"(see previous link for the list)produces Poisson ing CMP induces a Conway-Maxwell-Poisson distribution that is Poisson when its coefficient is0and geometric when its coefficient is1.@details Three proposal functions are currently implemented,two of them designed to improve mixing for sparse networks.They can can be selected via the MCMC.prop.weights=control param-eter.The sparse proposals work by proposing a jump to0.Both of them take an optional proposal argument p0(i.e.,MCMC.prop.args=list(p0=...))specifying the probability of such a jump. However,the way in which they implement it are different:•"random":Select a dyad(i,j)at random,and draw the proposal y⋆i,j∼Poisson=yi,j (y i,j+0.5)(a Poisson distribution with mean slightly higher than the current value and conditional on not proposing the current value).•"0inflated":As"random"but,with probability p0,propose a jump to0instead of a Poisson jump(if not already at0).If p0is not given,defaults to the"surplus"of0s in the observed network,relative to Poisson.•"TNT":(the default)As"0inflated"but instead of selecting a dyad at random,select a tie with probability p0,and a random dyad otherwise,as with the binary TNT.Currently,p0 defaults to0.2.zach7Usage#PoissonSee AlsoergmReference for index of reference distributions currently visible to the package.zach Karate club social network of Zachary(1977)DescriptionZachary(1977)reported observations of social relations in a university karate club,with mem-bership that varied between50and100,of whom34individuals:32ordinary club members and officers,the club president("John A."),and the part-time instructor("Mr.Hi");consistently in-teracted outside of the club.Over the course of the study,the club divided into two factions,and, ultimately,split into two clubs,one led by Hi and the other by John and the original club’s offi-cers.The split was driven by a disagreement over whether Hi could unilaterally change the level of compensation for his services.FormatThe data are represented as a network object,with an edge attribute contexts,giving the number of contexts of interaction for that pair of actors.In addition,the following vertex attributes are provided:list("club")the club in which the actor ended up;:the club in which the actor ended up;list("faction")faction alignment of the actor as recorded by Zachary:faction alignment of the actor as recorded by Zacharylist("faction.id")faction alignment coded numerically,as−2(strongly Mr.Hi’s),−1(weakly Mr.Hi’s),0(neutral),+1(weakly John’s),and+2(strongly John’s);list("role")role of the actor in the network(Instructor,Member,or President)DetailsZachary identifies the faction with which each of the34actors was aligned and how strongly and reports,for each pair of actors,the count of social contexts in which they interacted.The8contexts recorded were•academic classes at the university;•Hi’s private karate studio in his night classes;•Hi’s private karate studio where he taught on weekends;•student-teaching at Hi’s studio;•the university rathskeller(bar)located near the karate club;8zach•a bar located near the university campus;•open karate tournaments in the area;and•intercollegiate karate tournaments.The highest number of contexts of interaction for a pair of individuals that was observed was7.SourceZachary,WW(1977).An Information Flow Model for Conflict and Fission in Small Groups.Journal of Anthropological Research,33(4),452-473.Sociomatrix in machine-readable format was retrieved from http://vlado.fmf.uni-lj.si/pub/ networks/data/ucinet/ucidata.htm.ReferencesZachary,WW(1977).An Information Flow Model for Conflict and Fission in Small Groups.Journal of Anthropological Research,33(4),452-473.Examplesdata(zach)oldpal<-palette()palette(gray((1:8)/8))plot(zach,vertex.col="role",displaylabels=TRUE,edge.col="contexts")palette(oldpal)#Fit a binomial-reference ERGM.zach.fit1<-ergm(zach~nonzero+sum+nodefactor("role",base=2)+absdiffcat("faction.id"),response="contexts",reference=~Binomial(8))mcmc.diagnostics(zach.fit1)summary(zach.fit1)##Not run:#This is much slower.zach.fit2<-ergm(zach~nonzero+sum+nodefactor("role",base=2)+transitiveties,response="contexts",reference=~Binomial(8),eval.loglik=FALSE)mcmc.diagnostics(zach.fit2)summary(zach.fit2)##End(Not run)ZIPoisson-ergmProposal9 ZIPoisson-ergmProposalTODODescriptionTODODetailsThis proposal is not referenced in the lookup table.Index∗bipartiteBinomial-ergmReference,3Disc-ergmProposal,5DiscTNT-ergmProposal,5Geometric-ergmReference,6Poisson-ergmReference,6ZIPoisson-ergmProposal,9∗datasetszach,7∗directedBinomial-ergmReference,3CMB-ergmTerm,4CMP-ergmTerm,4Disc-ergmProposal,5DiscTNT-ergmProposal,5Geometric-ergmReference,6Poisson-ergmReference,6ZIPoisson-ergmProposal,9∗discreteBinomial-ergmReference,3Disc-ergmProposal,5DiscTNT-ergmProposal,5Geometric-ergmReference,6Poisson-ergmReference,6ZIPoisson-ergmProposal,9∗finiteBinomial-ergmReference,3∗modelsergm.count-package,2∗nonnegativeBinomial-ergmReference,3CMB-ergmTerm,4CMP-ergmTerm,4Geometric-ergmReference,6Poisson-ergmReference,6ZIPoisson-ergmProposal,9∗packageergm.count-package,2∗undirectedBinomial-ergmReference,3CMB-ergmTerm,4CMP-ergmTerm,4Disc-ergmProposal,5DiscTNT-ergmProposal,5Geometric-ergmReference,6Poisson-ergmReference,6ZIPoisson-ergmProposal,9∗valuedBinomial-ergmReference,3Disc-ergmProposal,5DiscTNT-ergmProposal,5Geometric-ergmReference,6Poisson-ergmReference,6ZIPoisson-ergmProposal,9Binomial-ergmReference,3,5CMB-ergmTerm,4CMP,2,6CMP-ergmTerm,4Disc-ergmProposal,5,5DiscTNT-ergmProposal,5,5DiscUnif-ergmReference,5ergm,2ergm.count,2ergm.count-package,2ergmReference,2,3,6,7ergmTerm,2,3Geometric-ergmReference,5,6InitErgmReference.Binomial(Binomial-ergmReference),3 InitErgmReference.Geometric(Geometric-ergmReference),6 InitErgmReference.Poisson(Poisson-ergmReference),6 10INDEX11 InitWtErgmProposal.Disc(Disc-ergmProposal),5InitWtErgmProposal.DiscTNT(DiscTNT-ergmProposal),5InitWtErgmProposal.ZIPoisson(ZIPoisson-ergmProposal),9InitWtErgmTerm.CMB(CMB-ergmTerm),4InitWtErgmTerm.CMP(CMP-ergmTerm),4network,7Poisson-ergmReference,5,6simulate.ergm,2sum,6TNT-ergmProposal,5valued ERGM terms,3,6zach,7ZIPoisson-ergmProposal,9。
英语选择题及答案解析
英语选择题及答案解析【篇一：英语语法练习题(答案详解)】xt>1. ms nancy didnt mind at all ______ to the ceremony.a. being not invitedb. not being invitedc. not invitingd. not to be invitedb2. _____ your meeting is! he offered them his sincere congratulations.a. how a great successb. what a great successc. how great successd. what great successb success 名词，保留远动词含义成功是不可数名词；如用来代替具体的人（成功者）或具体的事（成功的事情（东西））是可数名词。
故排除c,d；a中how是副词，如改成how great a success 就是正确的。
3. we must remember that _____fashion is not the most important thing in _______ life.a. /; theb. /; /c. the; /d. the; theb 抽象名词不特指时，前不用冠词。
4. it _____ quite a few years _____ the accused was declared innocent and set free.a. was; sinceb. is; thatc. will be; whend. was; befored 如将a项中was, since改成is, since是正确的；即从句中谓语先发生。
如用b项，是强调句，而强调句前后两个谓语动词在时间上必须一致（a）；被强调部分能还回原句中（b），即因为句中was declared是过去时, b项中is改成was；因为句中was declared是非延续性动词，在years后加上ago将一段时间变成一点就是正确的。
乔尔格林布拉特：投资神奇公式
乔尔·格林布拉特[复制链接]kljbzenkljbzen当前离线积分5591IP卡狗仔卡554主题4210帖子5591积分注册时间2008-11-9精华10版主积分5591威望124 点在线时间3262 小时凌通币2355最后登录2014-7-8发消息电梯直达1#发表于2014-2-16 17:28|只看该作者分享到：马上注册，享用更多功能您需要登录才可以下载或查看，没有帐号？欢迎来凌通价值网注册x投机是客观的，用固定的交易系统和适合自己的资金管理系统，抛弃主观看法往往效果惊人。
而投资是主观的，因为任何一个企业的估值不是一个可以精确定量的东西，而即使定性正确，如果定量的时候，对于“安全边际”估计的不足，那也会导致收益率天壤之别。
那么，有没有什么办法，对价值投资进行定性和定量相结合的机械性的方法？！换句话说，把这件看上去“复杂”的事，完全简化？答案就是“神奇公式”，发明者是：乔尔·格林布拉特。
乔尔·格林布拉特是Gotham资本公司的创始人和合伙经理人,自1985年这一私人投资公司成立以来,它的年均回报率达到了40%。
他不仅是哥伦比亚大学商学院的客座教授,一家《财富》500强公司的前董事长,价值投资者俱乐部网站()的合作发起人,还是《股市稳赚》一书的作者。
格林布拉特拥有理学学士学位,并从沃顿学院获得工商管理硕士学位。
他所创办的Gotham Capital公司，在过去20年创下了年平均40%的高投资报酬率。
更重要的是，他研究出一套简单的神奇公式，利用这个公式，可以从美国3,500家企业中筛选出最好的标的来投资，让掌管120亿美元资金的他，创造出优异的绩效。
请再看一眼他用简单的神奇公式，创造的业绩——年均回报率40%！相信老的市场玩家，都清楚这个成绩的可怕之处。
神奇公式——完全遵从价值投资的本质：用便宜的价格买好企业如何定义好企业？乔尔·格林布拉特认为，好企业就是资本回报率高（ROIC）的企业。
怀念威廉·科恩劳尔的尼瓦达银腾打印目录与检查表
Las Vegas
Year Guide
MM .999 Released Price
CC Rim 1994 $22-$28
(V) Ali Baba (3 Dots)
Aladdin on Carpet
CC Rim 1994 $100-150
Sinbad
Aladdin on Carpet
$18.00 $15.60
$17.00
$22.75
Approx
2019
2020 Silver
Auction Auction Weight
$18-$25 $16-$20 .6010 Oz
.4898 Oz
$16.50 $25.00 .4948 Oz
$16-$20 $20.00 .5881 Oz
$15-$25
Monorail
Bally's (3 7s)
GDC Rim 1995 $22-$28
Running 7 (LV Top)
Bally's (3 7s) (LV Top)
GDC Rim 1995 $22-$28
(E) Running 7(WR)(LV NV.Bottom) Bally's (3 7s) (LV Top)
Reno
MM .999
G Rim
Year Guide Released Price
1996 $22-$28
Toucan/Angel Fish
Atlantis Hotel Tower
G Inner 1998 $22-$28
(E) Toucan/Angel Fish(50++)
Atlantis (Many Blds) (WL)
statistics-2 by keller
CHAPTER 2GRAPHICAL AND TABULAR DESCRIPTIVE TECHNIQUESSECTIONS 1MULTIPLE CHOICE QUESTIONSIn the following multiple-choice questions, please circle the correct answer.1. Which of the following statements is false?a.All calculations are permitted on interval datab.All calculations are permitted on nominal datac.The most important aspect of ordinal data is the order of the data valuesd.The only permissible calculations on ordinal data are ones involving a rankingprocessANSWER: b2. The average number of units earned per semester by college students is suspected to berising. A researcher at Boston College wishes to estimate the number of units earned by students during the spring semester of 2004 at Boston. To do so, he randomly selects 250 student transcripts and records the number of units each student earned in the spring term of 2004. The variable of interest to the researcher is thea.number of students enrolled at Boston College during the spring term of 2004b.average indebtedness of Boston College students enrolled in the springc.age of Boston College students enrolled in the springd.number of units earned by Boston College students during the spring term of 2004ANSWER: d14 Chapter Two3. The classification of student major (accounting, economics, management, marketing,other) is an example ofa. a categorical random variable.b. a discrete random variablec. a continuous random variabled. a parameter.ANSWER: a4. A study is under way in national forest to determine the adult height of pine trees.Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 50 feet tall. It is estimated that the forest contains 32,000 adult pines.The study involves collecting heights from 500 randomly selected adult pine trees and analyzing the results. The variable of interest in the study is thea.age of a pine tree in the national forest.b.height of a pine tree in the national forest.c.number of pine trees in the national forest.d.species of trees in the national forest.ANSWER: b5. The classification of student class designation (freshman, sophomore, junior, senior) is anexample ofa. a categorical random variable.b. a discrete random variable.c. a continuous random variable.d. a parameter.ANSWER: a6. Most analysts focus on the cost of tuition as the way to measure the cost of a collegeeducation. But incidentals, such as textbook costs, are rarely considered. A researcher at Ferris State University wishes to estimate the textbook costs of first-year students at Ferris. To do so, he monitored the textbook cost of 200 first-year students and found that their average textbook cost was $275 per semester. The variable of interest to the researcher is thea.textbook cost of first-year Ferris State University students.b.year in school of Ferris State University students.c.age of Ferris State University students.d.cost of incidental expenses of Ferris State University students.ANSWER: aGraphical and Tabular Descriptive Techniques 15 7. The manager of the customer service division of a major consumer electronics companyis interested in determining whether the customers who have purchased a videocassette recorder made by the company over the past 12 months are satisfied with their products.The possible responses to the question “Are you happy, indifferent, or unhappy with the p erformance per dollar spent on the videocassette recorder?” are values from aa.discrete numerical random variable.b.continuous numerical random variablec.categorical random variable.d.parameter.ANSWER: c16 Chapter TwoTRUE / FALSE QUESTIONS8. There are actually four types of data: nominal, ordinal, interval, and ratio. However, forstatistical purposes, there is no difference between interval and ratio data, and the authors of your book combine the two types.ANSWER: T9. Quantitative variables usually represent membership in groups or categories.ANSWER: F10. Interval data, such as heights, weights, and incomes, are also referred to as quantitative ornumerical data.ANSWER: T11. Nominal data are also called qualitative or categorical data.ANSWER: T12. ATP singles rankings for tennis players is an example of an interval scale.ANSWER: F13. Interval data may be treated as ordinal or nominal.ANSWER: T14. Nominal data may be treated as ordinal or intervalANSWER: F15. Professor Hogg graduated from the University of Iowa with a code value = 2 whileProfessor Maas graduated from Michigan State University with a code value = 1. The scale of measurement likely represented by this information is interval.ANSWER: F16. Ordinal data may be treated as interval but not as nominal.ANSWER: F17. A variable is some characteristic of a population, while data are the observed values of avariable based on a sample.ANSWER: F18. An automobile insurance agent believes that company “A” is more reliab le than company“B”. The scale of measurement that this information represents is the ordinal scale.ANSWER: TGraphical and Tabular Descriptive Techniques 17 STATISTICAL CONCEPTS & APPLIED QUESTIONS19. The Dean of Students conducted a survey on campus. SAT score in mathematics is anexample of a __________, or __________ variable.ANSWER:quantitative, numerical20. Provide one example for nominal, ordinal, and interval data.ANSWER:Nominal data example: Political party affiliation for voters recorded using the code: 1 = Democrat, 2 = Republican, and 3 = Independent.Ordinal data example: Response to market research survey measured on the Likert scale using the code: 1 = Strongly agree, 2 = Agree, 3 = Neutral, 4 = Disagree, and 5 = Strongly disagree.Interval data example: Temperature in tennis courts during the US Open21. The dean of students conducted a survey on campus. The gender of the student is anexample of a __________, or __________ variable.ANSWER:categorical, qualitative22. For each of the following examples, identify the data type as nominal, ordinal, or interval.a.The letter grades received by students in a computer science classb.The number of students in a statistics coursec.The starting salaries of newly Ph.D. graduates from a statistics programd.The size of fries (small, medium, large) ordered by a sample of Burger Kingcustomerse.The college you are enrolled in (Arts and science, Business, Education, etc.)ANSWER:a.Ordinalb.Intervalc.Intervald.Ordinale.Nominal23. The Dean of Students conducted a survey on campus. Class designation (Freshman,Sophomore, Junior, and Senior) is an example of a __________, or __________ variable.ANSWER:categorical, qualitative18 Chapter Two24. Most colleges admit students based on their achievements in a number of different areas.The grade obtained in senior level English course (A, B, C, D, or F) is an example of a __________, or __________ variable.ANSWER:categorical, qualitative25. At the end of an escorted motor coach vacation, the tour operator asks the vacationers torespond to the questions listed below. For each question, determine whether the possible responses are interval, nominal, or ordinal.a.How many escorted vacations have you taken prior to this one?b.Do you feel that the stay in New York was sufficiently long?c.Which of the following features of the hotel in New York did you find most attractive:location, facilities, room size, or price?d.What is the maximum number of hours per day that you would like to spend traveling?e.Would your overall rating of this tour be excellent, good, fair, or poor?ANSWER:a.Intervalb.Nominalc.Nominald.Intervale.Ordinal26. For each of the following, indicate whether the variable of interest would be nominal orinterval.a.Whether you are a US citizenb.Your marital statusc.Number of cars in a parking lotd.Amount of time you spend per week on your homeworke.Lily’s travel time from her dorm to the student union at the university of Iowaf.Heidi’s favorite brand of tennis balls.ANSWER:a.Nominalb.Nominalc.Intervald.Intervale.Intervalf.Nominal27. In purchasing a used automobile, there are a number of variables to consider. The age ofthe car is an example of a __________, or __________ variable.Graphical and Tabular Descriptive Techniques 19 ANSWER:quantitative, numerical28. In purchasing an automobile, there are a number of variables to consider. The body styleof the car (sedan, coupe, wagon, etc.) is an example of a __________, or __________ variable.ANSWER:categorical, qualitative29. Before leaving a particular restaurant, customers are asked to respond to the questionslisted below. For each question, determine whether the possible responses are interval,nominal, or ordinal.a.What is the approximate distance of the restaurant from your residence?b.Have you eaten at the restaurant previously?c.On how many occasions have you eaten at the restaurant previously?d.Which of the following attributes of the restaurant do you find most attractive: service,prices, quality of the food, or varied menu?e.Would your overall rating of the restaurant be excellent, good, fair, or poor?ANSWER:a.Intervalb.Nominalc.Intervald.Nominale.Ordinal20 Chapter TwoSECTION 2MULTIPLE CHOICE QUESTIONSIn the following multiple-choice questions, please circle the correct answer.30. The best type of chart for comparing two sets of categorical data is aa.line chartb.pie chartc.histogramd.bar chartANSWER: d31. Which of the following statements about pie charts is false?a.Pie charts are graphical representations of the relative frequency distributionb.Pie charts are usually used to display the relative sizes of categories for interval data.c.Pie charts always have the shape of a circled.Area of each slice of a pie chart is the proportion of the corresponding category of thefrequency distribution of a categorical variableANSWER: b32. The two graphical techniques we usually use to present nominal data area.bar chart and histogramb.pie chart and ogivec.bar chart and pie chartd.histogram and ogiveANSWER: c33. Which of the following statements is false?a. A bar chart is similar to a histogramb. A pie chart is a circle subdivided into slices whose areas are proportional to thefrequenciesc.Pie charts emphasize the frequency of occurrences of each category in a frequencydistributiond.None of the aboveANSWER: c34. Which of the following statements is true?a.Bar charts focus the attention on the frequency of the occurrences of the categoriesb. A bar chart is created by drawing a rectangle representing each categoryc.The height of each rectangle in a bar chart represents the frequency for a particularcategoryd.All of the aboveANSWER: dGraphical and Tabular Descriptive Techniques 21TRUE / FALSE QUESTIONS35. A bar chart is used to represent interval data.ANSWER: F36. One of the advantages of a pie chart is that it clearly shows that the total of all thecategories of the pie adds to 100%.ANSWER: T37. The bar chart is preferred to the pie chart, because the human eye can more accuratelyjudge length comparisons against a fixed scale (as in a bar chart) than angular measures (as in a pie chart).ANSWER: T38. Bar and pie charts are graphical techniques for nominal data. The former focus theattention on the frequency of the occurrences of the categories, and the later emphasize the proportion of occurrences of each category.ANSWER: T39. Bar and pie charts are two graphical techniques that can be used to represent nominal data.ANSWER: T40. A bar chart is similar to a histogram in the sense that the bases of the rectangles arearbitrary intervals whose centers are the midpoints of the intervals.ANSWER: F41. If we wish to emphasize the relative frequencies for nominal data, we draw a histograminstead of drawing a bar chart.ANSWER: F42. Pie and bar charts are used widely in newspapers, magazines, and business andgovernment reports.ANSWER: T43. The size of each slice in a pie chart is proportional to the percentage corresponding to thatcategory.ANSWER: T44. A category that contains 30% of the observations is represented by a slice of a pie chartthat contains 100 degrees.ANSWER: F22 Chapter TwoSTATISTICAL CONCEPTS & APPLIED QUESTIONS45. Identify the type of data for which each of the following graphs is appropriate.a.Pie chartb.Bar chartANSWER:a.Nominalb.Nominal46. Voters participating in a recent election exit poll in Minnesota were asked to state theirpolitical party affiliation. Coding the data 1 for Republican, 2 for Democrat, and 3 for Independent, the data collected were as follows: 3, 1, 2, 3, 1, 3, 3, 2, 1, 3, 3, 2, 1, 1, 3, 2, 3, 1, 3, 2, 3, 2, 1, 1, and 3. Construct a frequency bar graph.ANSWER:FOR QUESTIONS 47 AND 48, USE THE FOLLOWING NARRATIVE:Narrative: Car DealersCar buyers were asked to indicate the car dealer they believed offered the best overall service. The four choices were Carriage Motors (C), Marco Chrysler (M), Triangle Auto (T), and University Chevrolet (U). The following data were obtained:T C C C U C M T C UU M C M T C M M C MT C C T U M M C C TT U C U T M M C U T47. {Car Dealers Narrative} Construct a frequency bar chart.ANSWER:48. {Car Dealers Narrative} Construct a pie chart. Which car dealer offered the best overallservice?It seems that Carriage Motors offered the best overall service.49. Given the following five categories and the number of times each occurs, draw a pie chartand a bar chart.ANSWER:FOR QUESTIONS 50 AND 51, USE THE FOLLOWING NARRATIVE:Narrative: Business School GraduatesThe frequency distribution for a sample of 200 business school graduates is shown in the following table.50. {Business School Graduates Narrative} Draw a pie chart of the number of graduates.ANSWER:51. {Business School Graduates Narrative} Draw a frequency bar chart.ANSWER:SECTION 3MULTIPLE CHOICE QUESTIONSIn the following multiple-choice questions, please circle the correct answer.52. The most appropriate type of chart for determining the number of observations at orbelow a specific value is:a. a histogramb. a pie chartc. a time-series chartd. a cumulative frequency ogiveANSWER: d53. In general, incomes of employees in large firms tend to bea.positively skewedb.negatively skewedc.symmetricd.All of the aboveANSWER:a54. The total area of the bars in a relative frequency histogram:a.depends on the sample sizeb.depends on the number of barsc.depends on the width of each bard.depends on the height of each barANSWER: c55. Which of the following statements is false?a. A frequency distribution counts the number of observations that fall into each of aseries on intervals, called classes that cover the complete range of observations.b.The intervals in a frequency distribution may overlap to ensure that each observationis assigned to an intervalc.Although the frequency distribution provides information about how the numbers inthe data set are distributed, the information is more easily understood and imparted bydrawing a histogramd.The number of class intervals we select in a frequency distribution depends entirelyon the number of observations in the data setANSWER: b56. The total area of the five bars in a relative frequency histogram for which the width ofeach bar is four units is:a. 5b. 4c.9d. 1ANSWER: b57. The relative frequency of a class is computed bya.dividing the frequency of the class by the number of classesb.dividing the frequency of the class by the class widthc.dividing the frequency of the class by the total number of observations in the data setd.subtracting the lower limit of the class from the upper limit and multiplying thedifference by the number of classesANSWER: c58. A modal class is the class that includesa.the largest number of observationsb.the smallest number of observationsc.the largest observation in the data setd.the smallest observation in the data setANSWER: a59. The sum of the relative frequencies for all classes will always equala.the number of classesb.the class widthc.the total number of observations in the data setd.oneANSWER: d60. When ogives or histograms are constructed, which axis must show the true zero or“origin”?a.The horizontal axis.b.The vertical axis.c.Both the horizontal and vertical axes.d.Neither the horizontal nor the vertical axis.ANSWER: b61. The width of each bar in a histogram corresponds to thea.differences between the lower and upper limits of the class.b.number of observations in each class.c.midpoint of each classd.frequency of observations in each class.ANSWER: a62. The most important and commonly graphical presentation of interval data is aa.bar chartb.histogramc.pie chartd.cumulative frequency distributionANSWER:b63. According to Sturges’ rule, the ideal number of class intervals in a frequency distributionof n = 150 data equals abouta.8b.15c.20d.28ANSWER: a64. According to Sturges’ rule, the ideal number of class intervals in a frequency distributionequalsa. 5b.15c. 3.3 + log (n), where n is the size of the data set.d. 1 + 3.3 log (n), where n is the size of the data set.ANSWER: d65. How many classes should a histogram contain if the number of observations is 250?a.5, 6, or 7b.7, 8, or 9c.9 or 10d.10 or 11ANSWER: c66. How many classes should a frequency distribution contain if the number of observationsis 45?a.5, 6, or 7b.7, 8, or 9c.9 or 10d.10 or 11ANSWER: a67. Sturge’s formula recommends that the number of class intervals to construct a frequ encydistribution or draw a histogram using a data set with n observations is determined by:a.log(n)b. 3.3 log(n)c. 1 + 3.3 log(n)d. 2 – 3.3 log(n)ANSWER: c68. Which of the following statements about number of modal classes is false?a. A unimodal histogram is one with a single peakb. A bimodal histogram is one with two peaks, not necessarily equal in heightc. A bimodal histogram is one with two peaks equal in heightd.None of the aboveANSWER: c69. Which of the following statements about shapes of histograms is true?a. A histogram is said to be symmetric if, when we draw a vertical line down the centerof the histogram, the two sides are identical in shape and sizeb. A positively skewed histogram is one with a long tail extending to the rightc. A negatively skewed histogram is one with a long tail extending to the leftd.All of the aboveANSWER: dTRUE / FALSE QUESTIONS70. A relative frequency distribution describes the proportion of data values that fall withineach class, and may be presented in a histogram form.ANSWER: T71. A relative frequency distribution describes the proportion of data values that fall withineach category.ANSWER: T72. The stem-and-leaf display reveals far more information relative to individual values thandoes the histogram.ANSWER: F73. Individual observations within each class may be found in a frequency distribution.ANSWER: F74. The following stem-and-leaf output has been generated by statistical software. Themedian of this data is 26.Stem-and-leaf of C2 N = 75Leaf Unit = 109 0 00011233314 0 5689921 1 000012326 1 6669933 2 3334445(8) 2 6667788834 3 002334427 3 5666999919 4 00012223310 4 5556667799ANSWER: F75. A cumulative frequency distribution lists the number of observations that are within orbelow each of the classes.ANSWER: T76. The following stem-and-leaf output has been generated by statistical software. This datahas a negative mode.Stem-and-leaf of C2 N = 75Leaf Unit = 0.011 -2 62 -2 05 -1 5558 -1 42022 -0 9999988777766536 -0 44322111111000(14) 0 0112223333334425 ************14 1 00222223344 1 562 2 03ANSWER: T77. Compared to the frequency distribution, the stem-and-leaf display provides more details,since it can describe the individual data values as well as show how many are in each group, or stem.ANSWER: T78. A histogram represents nominal data.ANSWER: F79. In the term “frequency distribution,” frequency r efers to the number of data values fallingwithin each class.ANSWER: T80. The class interval in a frequency distribution is the number of data values falling withineach class.ANSWER: F81. The largest value in a set of data is 140, and the lowest value is 70. If the resultingfrequency distribution is to have five classes of equal width, the class width will be 14.ANSWER: T82. A stem-and-leaf display describes two - digit integers between 20 and 70. For one of theclasses displayed, the row appears as 4|256. The numerical values being described are 24, 54, and 64.ANSWER: F83. The following “character histogram” has been generated by statistical software. Themedian class is 150.Histogram of C1 N = 75Midpoint Count-150 1 *-100 1 *-50 3 ***0 2 **50 7 *******100 12 ************150 18 ******************200 20 ********************250 5 *****300 5 *****350 1 *ANSWER: T84. The following stem-and-leaf output has been generated by statistical software. This dataset has a mean that is negative, and there is no modal class.Stem-and-leaf of C2 N = 10Leaf Unit = 0.102 - 1 534 - 0 97(2) - 0 654 0 33 0 62 1 31 1 8ANSWER: T85. A frequency distribution is a listing of the individual observations arranged in ascendingor descending order.ANSWER: F86. When a distribution has more values to the left and tails to the right, it is skewednegatively.ANSWER: F87. A histogram is said to be symmetric if, when we draw a vertical line down the center ofthe histogram, the two sides are identical in shape and size.ANSWER: T88. A skewed histogram is one with a long tail extending either to the right or left. Theformer is called negatively skewed, and the later is called positively skewed.ANSWER: F89. A bimodal histogram is one with two or more peaks equal in height.ANSWER: F90. A cumulative frequency distribution when presented in graphic form is called an ogive.ANSWER: T91. When a distribution has more values to the right and tails to the left, we say it is skewedpositively.ANSWER: F92. The sum of relative frequencies in a distribution always equals 1.ANSWER: T93. The stem-and-leaf display is often superior to the frequency distribution in that ismaintains the original values for the further analysis.ANSWER: T94. The sum of cumulative frequencies in a distribution always equals 1.ANSWER: F95. If the values of the sixth and seventh class in a cumulative frequency distribution are thesame, we know that there are no observations in the seventh class.ANSWER: T96. The larger the number of observations in a numerical data set, the larger the number ofclass intervals needed for a frequency distribution.ANSWER: T97. The original data values cannot be assessed once they are grouped into a frequencydistribution.ANSWER: T98. A research analyst was directed to arrange raw data collected on the yield of wheat,ranging from 40 to 90 bushels per acre, in a frequency distribution. He should choose 40 as the class interval width.ANSWER: F99. The relative frequency of a class is the frequency of that class divided by the total numberof classes.ANSWER: F100. Ogives are plotted at the midpoints of the class intervals.ANSWER: F101. Sturge’s formula recommends that the number of class intervals needed to draw a histogram using a data set with 200 observations is 12.79 which we round to 13.ANSWER: F102. A modal class is the class with the largest number of observations.ANSWER: T103. Incomes of employees in large firms tend to be negatively skewed, because there is a large number of relatively low –paid workers and a small number of well –paid executives.ANSWER: F104. The time taken by students to write exams is frequently positively skewed because few students hand in their exams early; most prefer to reread their papers and hand them in near the end of the scheduled test period.ANSWER: F105. A frequency distribution counts the number of observations that fall into each of a series of intervals, called classes that cover the range of observations.ANSWER: T106. One of the drawbacks of the histogram is that we lose potentially useful information by classifying the observations and sacrificing whatever information was contained in the actual observations.ANSWER: T107. The histogram is usually preferred over the stem – and – leaf display.ANSWER: F108. The stem – and –leaf display’s advantage over the histogram is that we can see the actual observations rather than observations classified into different classes.ANSWER: TSTATISTICAL CONCEPTS & APPLIED QUESTIONS109. Identify the type of data for which a Histogram is appropriate.ANSWER:Interval110. The total area under a relative frequency histogram for which the width of each class is ten units is _________.ANSWER:10111. Voters participating in a recent election exit poll in Minnesota were asked to state their political party affiliation. Coding the data 1 for Republican, 2 for Democrat, and 3 for Independent, the data collected were as follows: 3, 1, 2, 3, 1, 3, 3, 2, 1, 3, 3, 2, 1, 1, 3, 2, 3, 1, 3, 2, 3, 2, 1, 1, and 3. Develop a frequency distribution and a proportion distribution for the data. What does the data suggest about the strength of the political parties in Minnesota?ANSWER:Independent in Minnesota is stronger than Republican and Democrat partiesFOR QUESTIONS 112 THROUGH 118, USE THE FOLLOWING NARRATIVE: Narrative: Salespersons’ AgesThe ages of a sample of 25 salespersons are as follows:47 21 37 53 2840 30 32 34 2634 24 24 35 4538 35 28 43 4530 45 31 41 56112. {Salespersons’ Ages Narrative} Draw a histogram with four classes.ANSWER:113. {Salespersons’ Ages Narrative} Draw a histogram with six classes.ANSWER:114.{Sal espersons’ Ages Narrative} Draw a stem and leaf display.ANSWER:115.{Salesperson’s Ages Narrative} Construct an ogive for the data.ANSWER:116. {Salesperson’s A ges Narrative} Estimate the proportion of salespersons who are less than30 years of age.ANSWER:0.24117. {Salesperson’s Ages Narrative} Estimate the proportion of salespersons who are morethan 40 years of age.ANSWER:1-0.64 = 0.36118. {Salesp erson’s Ages Narrative} Estimate the proportion of salespersons who are between40 and 50 years of age.ANSWER:0.92 - 0.64 = 0.28。
凯勒势函数
凯勒势函数凯勒势函数是一种相对于群法的求解结构的势函数。
凯勒势函数是数学物理中的一个重要概念，它通过构造一种把结构离散化之后的群上的离散Laplace算子和随机高斯噪声向量来计算出对应的凯勒势函数。
凯勒势函数在信息论、统计力学、计算机科学等领域都有广泛的应用，尤其是在优化问题中的应用更为广泛。
凯勒势函数可以帮助研究者理解一个系统的内在结构，并用来描绘一个系统的参数空间。
同时，它也可以帮助研究者优化一个系统，找出一个最优解，或是构建一个最好的模型。
在实际使用中，凯勒势函数需要满足一定的性质。
首先，凯勒势函数需要满足可微性和可积性，这样才能运用梯度下降算法和共轭梯度算法等方法来求解问题。
其次，凯勒势函数需要满足正定性，这样才能保证优化结果是全局最优解。
凯勒势函数的有趣之处在于，它同时具有一种确定性和随机性。
凯勒势函数所描述的系统可以被看做是一个由结构和噪声组成的复合系统。
结构部分被视为确定性部分，而噪声部分则被视为随机性部分。
凯勒势函数具有的这种具有确定性和随机性的特点，使得它在许多应用领域中有着不同寻常的性能。
例如，在深度神经网络中，凯勒势函数被用来刻画神经网络中的结构和噪声，从而帮助研究者优化神经网络的结构和参数。
在统计力学中，凯勒势函数被用来描述一个系统的内在结构和粒子运动的性质。
在这里，凯勒势函数通常被称为“配分函数”，它是用来计算统计力学中各个粒子的位置、动量和能量的量。
除此之外，在最优化问题中，凯勒势函数也是一种非常优秀的工具。
通过建立凯勒势函数，我们可以优化一个系统并找出最佳的解决方案。
总之，凯勒势函数是一种非常强大的分析工具，它有着广泛的应用，能够处理许多不同的问题。
凯勒势函数的概念已经应用于许多领域，例如数学物理、信息与通信、计算机科学等，并且它的应用前景是广阔的。
凯勒势函数
凯勒势函数凯勒势函数（Keller Potential）是一种常用于描述粒子受势能影响下运动的数学模型。
它可以用于解决非常规势场或自由粒子的运动问题，广泛应用于物理学、量子力学、量子化学等领域。
凯勒势函数是由奥地利物理学家凯勒（Herbert Keller）在20世纪60年代提出的。
它可以用于描述一个粒子在某个给定势能场中的波函数，即粒子在这个势能场中的量子态。
凯勒势函数的数学表达式如下：Ψ(x) = A * exp(-2πα * F(x))其中Ψ(x)表示波函数，A是归一化系数，α是与粒子的质量和普朗克常数有关的常数，F(x)表示势能场。
凯勒势函数可以通过解薛定谔方程来求得。
方程的形式为：E * Ψ(x) = [-((h^2/8π^2m) * ∇^2 + V(x))] * Ψ(x)其中，E是能量，h是普朗克常数，m是粒子的质量，V(x)是势能函数。
凯勒势函数的优势在于它可以通过解析方法求解问题，简化了计算过程。
这使得凯勒势函数在描述复杂势场下的物理过程中具有很高的适用性。
例如，在核物理中，凯勒势函数被用于描述核子的弹性散射；在量子化学中，它可以用来描述分子间的相互作用；在固体物理中，它可以用来研究电子在晶格中的运动。
除了解决量子力学问题外，凯勒势函数还被应用于实际的科学研究和工程计算中。
例如，在材料科学中，凯勒势函数可以用于计算材料的电子结构和能带结构；在计算物理学中，凯勒势函数可以用于模拟粒子在任意势能场下的运动轨迹。
凯勒势函数的物理意义在于它可以描述粒子在势能场中的概率分布。
通过计算波函数的模方，我们可以得到粒子在空间中不同位置的概率密度。
这可以用来解释物理实验中观测到的现象，并为进一步的理论研究提供了基础。
总之，凯勒势函数是一种重要的数学模型，它在解决非常规势场或自由粒子的运动问题中具有广泛的应用价值。
它不仅在理论物理学中有重要地位，而且在实际科学研究和工程计算中也发挥着重要作用。
它的提出和应用为我们理解微观世界的物理现象和开展相关研究提供了重要的数学工具。
Statistics - the science of collecting, organizing
IntroductionStatistics - the science of collecting, organizing, analyzing, and interpreting Data.Chapter 1: Collecting DataChapter 2: Organizing/Analyzing DataChapters 3-8: Interpreting DataTypes of Data SetsPopulation - data set consisting of all outcomes, measurements, or responses of interest Sample - data set which is a subset of the population data setExamples:•If we are interested in measuring the salaries of American high-school teachers, the population data set would be a list of the salaries of every high-school teacher in America. A sample data set could be obtained by selecting 100 high-schoolteachers from a across the country and listing their salaries.• A polling organization wants to know whether Americans favor increased defense spending. The population data set would consist of the responses of everyAmerican. A common way of choosing a sample data set would be to randomlycall 1000 Americans and gather their responses to the question of whether theyfavor increased defense spending.• A biologist wants to measure the weights of female Alaskan grizzly bears. What would be the population data set? A possible sample set?Types of MeasurementsParameter - a numerical measurement made using the population data setStatistic - a numerical measurement made using a sample data setExamples:•Using the teacher salary data sets, we could calculate the average salary for the high-school teachers. The average calculated from the population data set would be the parameter. The average calculated from the sample of 100 teachers would be a statistic.•Using the opinion poll data on defense spending, we could calculate the percentage of Americans who favor increased defense spending. The actualpercentage of all Americans who favored increased defense spending would bethe parameter. The percentage of the 1000 Americans in our sample who favored increased spending would be a statistic.Notice that unless the population is very small it is probably impossible to gather the population data set, and so it is usually impossible to calculate the parameter we are interested in.The main idea of the science of statistics is that we can get around this difficulty by selecting a sample, calculating the sample statistic, and use the sample statistic to make an estimate of the parameter.Unfortunately, statistical estimates can never be 100% certain. (But they can be 90% or 95% or 99% certain)Types of DataQualitative Data - non-numerical characteristics or labelsExamples: Eye Color, First NameFavorite Movie, Political PartyQuantitative Data - numerical measurements or quantitiesExamples: Height, Weight, IncomeResting Pulse Rate, Blood Alcohol LevelLevels of MeasurementNominal Data– Can be qualitative only. Data values serve as labels, but the labels have no meaningful order.Examples:Blood Type, College Major, Breed of DogShape of Bacteria in a Petri DishOrdinal Data– Can be qualitative or quantitative. Data values serve as labels but the labels have a natural meaningful order. Differences between values, however, are meaningless.Examples:Statistics Grade, NCAA Basketball RankingsTerror Threat LevelInterval Data– Are always quantitative. Data values are numerical, so they have a natural meaningful order, and differences between data values are meaningful. The ratio of two data values, however, is meaningless. This occurs when zero is an arbitrary measurement rather than actually indicating “nothing”.Examples:Temperature, Year of BirthRatio Data– Are always quantitative. Data values are numerical, have order, and both differences and ratios between values are meaningful. Zero measurement indicates absence of the quantity being measured.Examples:Weight, Height, Volume, Number of ChildrenMethods of Data CollectionMethodCensus - collect measurements from the entire populationUsed when population is small. Sampling - choose a sample from your population and collect measurements from sample.Used when population is large. (Most Common)Simulation - Program a computer with a mathematical or physical model to simulate population data.Used when impossible to collect sample data.Experiment - Collect a sample, split the sample into two groups:The Case Group receives treatment. The Control Group does not.Used to measure the effect of treatment by comparing the characteristics of the case and control groups.Additional Terms:Placebo,Placebo EffectSingle Blind ExperimentDouble Blind ExperimentExamples •Determine average grade on a Statistics exam•Measure salaries of all 50 state governors•Opinion Polls•Determine average income in U.S•Temperature at the core of the Sun•Monte Carlo Simulations• A sample of 200 cancer patients is selected. An experimentaldrug is given to 100 patients andthe remaining 100 patientsreceive a placebo. The survivalrates of the two groups are thencomparedMethods of SamplingMethodRandom Sampling - The sample is chosen as a result of chance occurrences Systematic Sampling - The population is placed on a list, a random starting point is chosen and then every k-th member is selected.Stratified Sampling - The population is divided into groups (strata) usually with meaningful differences, and a sample is chosen from each group.Cluster Sampling - The population is divided into groups in a more or less random way, and then a sample is chosen by randomly selecting entire groups.Convenience Sampling - Choose individuals for a sample because they are easy to include.Examples •Telephone polling randomtelephone numbers•Drawing names out of a hat •Choosing a sample of registered voters by choosing every 25thvoter from the county registration roll•Testing every 300th product from the assembly line•Choosing 200 men and 200women for a sample•Stratify the population by income level and then choose a sample of low, middle, and high incomeindividuals•Randomly choose 10 polling stations in a city and exit poll allvoters at those stations •Internet Polls•Mail-In Customer Survey。
Extracting spectral density function of a binary composite without a-priori assumption
a r X i v :c o n d -m a t /0403243v 1 [c o n d -m a t .o t h e r ] 9 M a r 2004Extracting spectral density function of a binary composite without a-priori assumptionEnis Tuncer ∗Applied Condensed-Matter Physics,Department of Physics,University of Potsdam,D-14469Potsdam Germany(Dated:February 2,2008)The spectral representation separates the contributions of geometrical arrangement (topology)and in-trinsic constituent properties in a composite.The aim of paper is to present a numerical algorithm based on the Monte Carlo integration and contrainted-least-squares methods to resolve the spectral density function for a given system.The numerical method is verified by comparing the results with those of Maxwell-Garnett effective permittivity ter,it is applied to a well-studied rock-and-brine system to instruct its utility.The presented method yields significant microstructural information in improving our understanding how microstructure influences the macroscopic behaviour of composites without any intri-cate mathematics.PACS numbers:77.22.-d,77.22.Ch,02.70.Hm,02.70.Uu,05.10.Ln,07.05.Kf,61.18-jKeywords:Spectral representation,composites,dielectric permittivity,micro-structural informationTheory of mixtures and their electrical properties have attracted researchers to seek a relation between intrinsic properties of the parts forming the mixture (constituents)and their spatial arrangement inside the mixture[1].Bergman[4]has proposed a mathematical way for repre-senting the effective dielectric permittivity εe of a binary mixture as a function of permittivities of its constituents,ε1and ε2,and an integral equation,which includes the geometrical contributions.It is called the spectral den-sity representation (SDR).After the introduction of non-destructive measurement techniques and systems,such as electrical[2,3]or acoustic impedance spectroscopy[3],the impedance of materials (either pure or composite)could be recorded for various frequencies ν.Then,the frequency could be used as a probe to obtain microstructural informa-tion with the application of the SDR[5,6,7,8,9,10,11].This can only be achieved if (i )no influence of νon the geometrical arrangement of phases is present[12],and (ii )the intrinsic properties of phases are known as a function of ν.Numerical[8,9,10]and analytical[5,6,7]approaches have been used and proposed to resolve the spectral density function (SDF)for composites.Although numerical ap-proaches could be prefered over the analytical ones,which are emprirical expressions and are not universal,they solve a nontrivial—ill-posed—inverse problem[9].Here,we ap-ply a recently developed numerical method[13]to extract the SDF of a binary mixture.The method is based on the Monte Carlo integration and constrained-least-squares (C-LSQ)algorithms.By using this procedure the integration constant becomes continues rather than discrete as in reg-ulation algortihms.First,the verification of the proposed method is presented by considering the Maxwell-Garnett (MG)effective dielectric function[14].Later,it is applied to the dielectric data of a rock-and-brine system[15],which has been also used by Refs.5and 6to test their analytical expressions.For a binary composite system with constituent permit-tivities ε1and ε2,and concentrations q 1and q 2,(q 1+q 2=1),and with an effective permittivity εe ,the SDR is ex-FIG.1:Parametric plot of the scaled mixture permittivity.The symbols are the analytical model of Maxwell-Garnett equa-tion,and the solid lines (——)are the values calculated from the spectral functions obtained from the proposed numerical method.The semi-circles from large to small corresponds to q 2={0.95,0.7,0.5,0.3,0.05},respectively.The inset is the en-largement of the values close to the origin for q 2={0.05,0.30}.pressed as[16],∆e i /∆ji −A j =1g j (x )[1+ε−1i ∆ji x ]−1d x (1)where,∆ij =εi −εj ,and is complex and frequency de-pendent.A j is a constant,and depends on the concentra-tion and structure of the composite.The SDF is g (x ),andit is sought by the presented procedure.The SDF satisfies g j (x )d x =q j [4,10]and x g j (x )d x =q j q i /d ,where d is the dimension of the system.The shape of the inclu-sions in a matrix can also be related to d [17].Finally,x is called the depolarization factor.The numerical procedure is briefly as follows:first the integral in Eq.(1)is written in a summation form over some number of randomly selected (known)x n -values,x n ∈[0,1].This converts the non-linear problem in hand to a linear one with g j n being ter,a C-LSQ is applied to get the corresponding g j n -values:min ||∆−K g j n ||2and g j n ≥0(2)Typeset by REVT E X2FIG.2:Calculated spectral density distributions,which cor-respond to delta sequences.The spectral functions from leftto right corresponds to q2={0.95,0.7,0.5,0.3,0.05},re-spectively.The correcponding(calculated)A2values are {0.002,0.012,0.029,0.064,0.358},respectively,for the consid-ered concentrations.The dashed lines(–––)show the positionsof the actual delta-functions for the MG expression.where∆is the left-hand-side of Eq.(1),and K is the kernel-matrix,[1+ε−1i∆ji x n]−1.When this minimization is run over-and-over with new sets of x n-values,most prob-able g j n-values are obtained.For a large number of mini-mization loop,actually the x-axis becomes continues—the Monte Carlo integration hypothesis.Finally,the weighted distribution of g j n versus x n leads g(x)[18]. Application of the numerical procedure to the MG expression should yield delta function distributions for g(x)[5,10].The dielectric function for a d-dimensional (or composite with arbitrary shaped inclusions)MG com-posite is defined asεe=ε1[1+d q2∆21(q1∆21+dε1)−1].(3) The resulting SDF is then,g j(x)=δ[x−(1−q j)/d].(4) We choose the following values for dielectric functions of the phases:ε1=1−ı(100ε0ω)−1andε2=10−ı(ε0ω)−1withω=2πνandε0=8.854pF/m.The left-hand-side of Eq.(1)without the constant A2is plot-ted for a3-dimensional composite(d=3which cor-responds to spherical inclusions)in Fig.1as a parame-teric plot of the imaginary part of∆e1/∆21against its real part.The graph is a semi-circle for the MG expression. In thefigure,five different concentration levels are plotted, q2={0.05,0.3,0.5,0.7,0.95},the inset shows the en-largement close to the origin,which illustrates the low con-centrations,q2={.05,0.3}.The size of the semi-circles are proportional to the concentration of Phase2.The analy-ses performed on the scaled effective permittivity,Eq.(1), with the help of the applied method yield the solid lines (——)in thefigure.The corresponding g(x)are plotted in Fig.2on a log-log scale.In thefigure,the expected locations of g(x) from Eq.(4)are also shown with dashed lines(–––). The g(x)-distributions obtained are analized by the L´e vy distribution[19],which generates a delta-squence[20].The TABLE I:Comparison between the reults of the proposed nu-merical approach and those of the L´e vy statistics and the given analytical SDF for the MG effective permittivity expressions for various concentrations.The bars on the quantities indicate that they are calculated from the numerical results.q2x b q1/d c A2in d A2out e0.050.0530.3180.3160.0020.0020.0570.048 0.300.3010.2340.2330.0120.0130.2130.210 0.500.0500.1670.1670.0290.0290.2490.249 0.700.7040.1000.1000.0640.0640.2130.2800.950.9510.0170.0170.3580.3590.0510.048a Calculated using the resulting g2(x).Known from the definition of g j(x)—integral 10g j(x)d x is equal to this value.b The localization parameter for the calculated L´e vy distribution.The shape parameters and the amplitude of the L´e vy distributions are disregarded.c Known from the definition of the SDF for the MG expression,Eq.(4).c A2-value calculated before the numerical procedure using Eq.(1).d Mean A2-value calculated during each Monte Carlo integration step in the numerical procedure,Eq.(2).e Calculated using the resulting g2(x)and x-values.Known from the defi-nition ofg j(x)—the values is equal to the integral 103x g j(x)d x.FIG.3:Parametric plot of the scaled rock-and-brine permittiv-ity.The symbols(•)are the experimental data of Ref.15.The chain line(–·–)is the results for the same assumptions as Refs.5 and6.The solid(——)and dashed(–––)lines are results obtained by two different water and composite conductivities;σ2=0.85S/m andσe=0.041S/m(——),andσ2=0.85S/m andσe=0.038S/m(–––).solid lines(——)illustrate the appropriate L´e vy distribu-tions.Various parameters from the statistical analyses and their expected values are presented in Table I.The con-centration values,x are within <1%of the actual values stated by the proposed analyti-cal expression[5,10].Finally,the product of the concentra-tions3We also test our procedure on a rock-and-brine com-posite system[15],which has been studied by various scientists[5,6].The same assumptions as in Ref.5and6 are made to calculate the dielectric function of the brine (water-salt solution).The ohmic conductivity of the water is taken to beσ2=0.93S/m,later the dielectric function of the brine at T=75◦C is calculated by the following expression[5,6],ε′2(T)=94.88−0.2317T+0.000217T2S(T)=5.363[(T+7)(82σ2)−1−0.0123]−1.047ε′2(T,S)=[εw0−1+0.0417S(1000−S)−1]−1ε2(T,S)=ε′2(T,S)−ıσ2(ε0ω)−1(5) The relative permittivity of the rock is taken to be con-stant without any imaginary part,ε1=7.5.The result-ing scaled dielectric quantity in Eq.(1)is presented in Fig.3.Similar to Fig.1,a semi-circle-like shape is ob-served.Thefirst analysis with the above considerations results in an unsatisfactory calculatedεe as presented with the chain line(–·–)in Fig.4.The low frequency side (ω<30MHz)of the real permittivity has discrepancies. Therefore,the experience of the author regarding dielectric data analyses suggests that the measured values at the low frequencies do not particularly satisfy the Kramers-Kronig relations[13,21].Consequently,the application of the Kramers-Kronig relations yield lower effective compos-ite conductivity then the original data,σe=0.055S/m. Therefore,two different conductivities are adoptedσe= 0.041and0.038S/m,while we keep the conductivity of the water constant and lower than the previous consider-ationσ2=0.85S/m.With these parameters as inputs, the resulting effective permittivity values have better agree-ment with those of measurements.And if compared to the results of Stroud et al.[5]and Ghosh and Fuchs[6],our values have less residual than theirs.In Fig.5,the obtained g(x)are presented.It is striking that two very distinct peaks are observed whatever the ini-tial assumptions for the conductivities of the water as well as the composite are.The g(x)can be divided into three sub-SDF,which are located around x={0,0.004,0.04}. It is clear that the original data can be modeled by only two SDF as delta sequences[10,11,22]without a sophisti-cated mathematics.The SDF of Ref.6is also displayed as a comparison with the thick chain line(–·–),which has been valuable to give limits for the depolarization factor x.However,in the case of Kenyon’s data[15]it overes-timates the upper limit,which has been1.The two pe-culiar depolarization factors resolved from the peaks have concentrations of0.111and0.023,respectively,which are calculated from the L´e vy distributions.The low x-side of g(x)yields a very small concentration(∼10−5)for that particular depolarization process.If we take into ac-count the yielding concentrations of the brine in the system (q2≈0.134),we can state that the three peaks correspond to oblate to needle like porous structures of the brine withFIG.4:Measured(•from Ref.15)and re-calculated dielec-tric permittivityℜ(εe)and alternating current conductivityσe=ℑ(εeε0ω).The chain line(–·–)is the results for the same as-sumptions as Refs.5and6.The line legends are the same as inFig.3.FIG.5:Calculated spectral density distributions.The lines rep-resent the appropriatefitted L´e vy distributions,and their legendsare the same as in Fig.3.The thick chain line is the SDF g(x)ofRef.6.shape factor estimates d≈q1/4beginning.It is shown that it can resolve unique individual depolarization processes,which could indeed be used to obtain valuable microstructural information regarding the composite and its constituents in various researchfields,in which impedance spectroscopy is used for characterization of materials,such as,polymeric,pharmaceutical,biologi-cal,building,colloidal,porous,etc.∗Electronic address:enis.tuncer@1For reviews on composites see:ndauer,in Electrical Transport and Optical properties of Inhomogeneous Media, edited by J.C.Garland and D.B.Tanner(AIP,New York, 1978),vol.40of AIP Conf Proc,pp.2–43: A.Priou,ed., Progress in Electromagnetics Research,Dielectric Proper-ties of Heterogeneous Materials(Elsevier,New York,1992): S.Torquato,Random Heterogeneous Materials:Microstruc-ture and macroscopic properties,vol.16(Springer-Verlag, Berlin,2001):M.Sahimi,Heterogeneous Materials I:Linear Transport and Optical Properties,vol.22(Springer-Verlag, Berlin,2003):ton,The Theory of Composites(Cam-bridge University Press,Cambridge UK,2002).2A.K.Jonscher,Dielectric Relaxation in Solids(London: Chelsea Dielectric,London,1983):J.R.Macdonald,ed., Impedance Spectroscopy(John Wiley&Sons,New York, 1987).3N.G.McCrum,B.E.Read,and G.Williams,Anelastic and Dielectric Effects in Polymeric Solids(John Wiley&Sons Ltd.,London,1967),dover ed.4D.J.Bergman,Phys Rep43(9),377(1978):D.J.Bergman, Phys Rev B19(4),2359(1979): D.J.Bergman,Ann Phys 138,78(1982).5D.Stroud,ton,and B.R.De,Phys Rev B34(8), 5145(1986).6K.Ghosh and R.Fuchs,Phys Rev B38(8),5222(1988).7S.Barabash and D.Stroud,J Phys:Cond Matt11,10323 (1999).8A.R.Day and M.F.Thorpe,J Phys:Cond Matt11,2551 (1999):A.R.Day,M.F.Thorpe,A.G.Grant,and A.J.Siev-ers,Physica B279,17(2000):A.R.Day,A.R.McGrun,D.J.Bergman,and M.F.Thorpe,Physica B338,24(2000).9E.Cherkaev and D.Zhang,Physica B338,16(2003).10A.V.Goncharenko,Phys Rev E68(041108),1(2003):A.V.Goncharenko,V.Z.Lozovski,and E.F.Venger,Opt Comm 174,19(2000).11Application of SDR to a biological system just using two poles is presented in J.Lei,J.T.K.Wan,K.W.Yu,and H.Sun,Phys Rev E64(012903),1(2001).12The geometry should be static at each frequency,meaning that no piezoelectricity exists in the constituents,and the elasticproperties of the phases should be the same or similar to each other otherwise there would be a nonzero displacement vec-tors(deformation)in the composite.13E.Tuncer and S.M.Guba´n ski,IEEE Trans Diel El Insul8, 310(2001): E.Tuncer,M.Furlani,and B.-E.Mellander,J Appl Phys(2004),in press.14J.C.Maxwell-Garnett,Phil Trans Royal Soc London A203, 385(1904).15W.E.Kenyon,J Appl Phys55(8),3153(1984).16Several different notations have been used in the literature[5, 6,8].Here,we rearrange the expression by Ref.6,and obtaina similar one those used by Refs.5and8.17The dielectric properties of a system with arbitrary ellip-soidal inclusions are given in R.Sillars,J IEE80,378 (1937):H.Fricke,J Phys Chem57,934(1953):W.R.Tinga,in Dielectric properties of heteregeneous materials(El-sevier,1992),vol.6of Progress in Electromagnetic Research, chap.1,pp.1–40.and E.Tuncer and S.M.Guba´n ski,Turk J Phys26,1(2001).The depolarization(shape)factors for various composite systems are calculated in these references.As an example,needle-like(prolate)inclusions parallel to the field direction yield d≫3,uni-direction cylindrical inclu-sions perpendicular to thefield direction yield d=2and oblate inclusions perpendicular to thefield yield d≈1.18This is achieved by dividing the x-axis in channels and aver-aging g jnin each channel.19The expression for the L´e vy statistics is L(x;A,x|)γ[1+ıξx/|x|tan(γπ/2)]}|,where ξ,ζ,andγare parameters that define the shape of the dis-tribution.A and。
Statistical Computing with R
1 Introduction to R
R and Splus are so-called object-oriented languages, which means roughly that they are organized to recognize both inputs and outputs (such as numerical data and fitted statistical models) from standard computer-representations, which have the structure primarily of lists (of basic data structures) with attributes of several special types. All-encompassing definitions are elusive, but the main idea is that outputs of onestage of analysis can be computed on and then inputted to furtherstages [including further model-fitting, pictures and graphs, etc.] without re-defining their structure. This makes R especially suited to interactive analysis.
load(‘‘Work.RData’’)
to make all of the contents of the workspace Work.RData available in the current session. (b) Exit R by typing q() following the R line-prompt > . If you want to save everything in the current area as an R workspace (say NewSpace.RData) for future reference, then before you quit, issue a command
高级微观经济学所需的数学知识及应用
Although all the three definitions on the upper semi-continuity at x0 are equivalent, the second one is easier to be versified.
A function f : X → R is said to be upper semi-continuous on X if f is upper semicontinuous at every point x ∈ X.
Theorem 1.2.2 (Separating Hyperplane Theorem) Suppose that A, B ⊂ Rm are convex and A ∩ B = ∅. Then, there is a vector p ∈ Rm with p ̸= 0, and a value c ∈ R such that
condition. Becoming a rich country also depends on other factors such as political system, social infrastructures, and culture. Additionally, no example of a country can be found so far that it is rich in the long run, that is not a market economy.
are closed subsets of X.
Let f be a function on Rk with continuous partial derivatives. We define the gradient
湖北省荆州市英语初三上学期期中试卷及解答参考
湖北省荆州市英语初三上学期期中模拟试卷及解答参考一、听力部分（本大题有20小题，每小题1分，共20分）1、听力材料：W: Good morning, everyone. How are you doing today?M: I’m fine, thank you. How about you?W: I’m doing well too. By the way, have you finished your English homework for this week?M: Not yet. I was planning to do it this evening.W: That sounds good. You should always try to keep up with your studies.M: Yes, I agree. It’s important to stay on top of things.Question: What did the student say about his English homework?A) He had finished it already.B) He planned to do it this evening.C) He didn’t need to do it.D) He didn’t have any homework.Answer: B) He planned to do it this evening.Explanation: The student explicitly states, “I was planning to do it this evening,” indicating that he had not yet finished his homework and intendedto complete it later that night.2、听力材料：W: I heard you’re going to visit the science museum this weekend.M: Yes, my science teacher arranged a field trip for our class. We’re all very excited to see the new exhibits.W: That sounds fascinating. Do you have a favorite subject in school?M: I think I enjoy math the most. It’s challenging, but I find it very rewarding.W: Math can be very interesting. Do you think you’ll ever study it at university?M: I’m not sure yet, but I’m considering majoring in engineering or computer science.Question: What is the student most interested in studying at university?A) EnglishB) ScienceC) MathematicsD) ArtAnswer: C) MathematicsExplanation: The student mentions that he enjoys math the most and is considering majoring in engineering or computer science, which are fields closely related to mathematics.3.You are listening to a conversation between two friends, Alice and Bob.They are discussing their weekend plans.W: Hey Bob, do you have any plans for this weekend?M: Well, I’m thinking of going hiking with my friends on Saturday morning. How about you, Alice?Q: What is Bob planning to do on Saturday morning?A. Go hiking with his friends.B. Go shopping with Alice.C. Have a movie night at home.D. Visit a museum.Answer: A. Go hiking with his friends.Explanation: In the conversation, Bob mentions that he is planning to go hiking with his friends on Saturday morning, which makes option A the correct answer.4.Listen to a short dialogue between a teacher and a student in the school library.T: Hi, John. I see you’re reading a book about history. Are you doing some research for a project?S: Yeah, actually. I’m working on a paper about the Roman Empire. Do you know any good sources I can use?Q: What is John doing in the library?A. Borrowing a book.B. Reading a book about history.C. Studying for a math test.D. Talking to the librarian.Answer: B. Reading a book about history.Explanation: In the dialogue, John mentions that he is reading a book about the Roman Empire, which indicates that he is reading a book about history. Therefore, option B is the correct answer.5、You hear a conversation between two students, Jack and Lily, discussing their weekend plans.Jack: “Hey Lily, what are you doing this weekend?”Lily: “I’m planning to go hiking with some friends. How about you, Jack?”Jack: “I was thinking of going to the movies with my brother. We haven’t seen each other in a while.”Lily: “That sounds fun! Maybe we can meet up after and grab some coffee?”Jack: “Sure, that sounds great. What time were you thinking?”Question: What does Lily plan to do this weekend?A) Go to the movies with her brotherB) Go hiking with some friendsC) Watch TV at homeD) Study for examsAnswer: B) Go hiking with some friendsExplanation: In the conversation, Lily says, “I’m planning to go hiking with some friends,” which indicates that she has a plan to go hiking with her friends over the weekend.6、You listen to a short interview with a local chef, Chef Maria, who talks about her cooking style and favorite dish.Interviewer: “Welcome to our show, Chef Maria. Can you tell us a little bit about your cooking style?”Chef Maria: “Absolutely. I believe in using fresh, local ingredient s to create unique dishes. I love to combine different flavors and spices to create something truly special.”Interviewer: “What’s your favorite dish to cook?”Chef Maria: “My favorite dish to cook is my signature paella. It’s a Spanish rice dish that combines chicken, seafood, and a variety of vegetables. The key is to use the right amount of saffron to give it that classic golden color and flavor.”Question: What is Chef Maria’s favorite dish to cook?A) SpaghettiB) PaellaC) PizzaD) TacosAnswer: B) PaellaExplanation: Chef Maria explicitly states, “My favorite dish to cook is my signature paella,” which makes it clear that paella is her favorite dish to prepare.7.You are listening to a conversation between two students, Alice and Bob,discussing their weekend plans.Alice: Hey Bob, what are your plans for this weekend?Bob: Well, I’m thinking of going hiking in the mountains. How about you, Alice? Alice: That sounds great! I’m actually planning to go to the beach with my friends.Bob: Oh, a beach trip sounds fun. Are you bringing any beach games?Alice: Yeah, we’re bringing some frisbees and a volleyball.Question: What is Bob’s plan for the weekend?A) Going to the beachB) Going hiking in the mountainsC) Visiting a museumD) Staying at homeAnswer: B) Going hiking in the mountains解析：在对话中，Bob提到他计划去山里远足，所以答案是B。
具有退化扩散的抛物—抛物keller-segel方程组全局弱解的存在性
具有退化扩散的抛物—抛物keller-segel方程组全局弱解的存在性几类退化Keller-Segel方程一致L~∞有界弱解的存在性现如今,随着交叉学科研究风靡全世界,越来越多的数学家开始关注其他学科的模型,例如生物模型,化学模型和物理模型.在这篇文章中,我们将研究一个非常有趣的关于细菌趋化性的生物数学模型:Keller-Segel模型.Keller-Segel模型是由Keller和Segel在1970年[1,2]提出的,它主要描述的是网柄菌的生物趋化性.在这个模型中,细菌被一种化学物质所吸引,并且可以释放出同一种化学物质.我们研究的主要目标是对于两种不同的退化Keller-Segel模型,证明其弱解的全局存在性.这篇文章的主要内容如下:在第一章中,我们介绍了Keller-Segel模型的背景信息.通过叙述原始模型的构造过程,我们希望读者能够更深入而全面的了解Keller-Segel模型.我们还列出了一些著名的简化模型以及优雅的结果,旨在向读者展示Keller-Segel模型的动人之处,从而吸引更多的人投身到研究中来.随后,我们陈述了此文灵感的来源,克服的困难以及得到的结论.我们还在这一章中给出了一些尚未解决的问题.在第二章中,我们研究了如下的退化抛物-抛物Keller-Segel模型:这里d≥3,扩散指数0m2-2/d其中,u(x,t)表示细菌的密度,v(x,t)表示化学物质的浓度.不失一般性地,我们假设v(x,0)=0,即最初的容器中并没有化学物质,随后由细菌产生.为了证明弱解的全局存在性,我们首先要得到先验估计.对于已经被广泛研究的退化抛物-椭圆Keller-Segel方程,具有最佳常数的Hardy-Littlewood-Sobolev不等式是进行估计的关键:然而在退化的抛物一抛物Keller-Segel方程中,HLS不等式不再适用,因为v(x,t)无法由基本解的形式表出.因此,我们利用半群理论代替HLS不等式进行先验估计.以下关于半群的定义及估计是标准的.考虑柯西问题:定义0.0.1.设T＞0，p≥1(?)以及(?).函数(?)满足是问题(2)在[0,T]上唯一的温和解.这里热半群算子et△为(?),其中G(x,t)是热核即(?)不难证明,上面定义的温和解也是方程的一个弱解.接下来,我们介绍一个著名的热核的最大Lp模正则性结论,它是进行先验估计的关键.引理0.0.1.假设1p+∞,T0.那么对每一个f∈Lp(0,T;Lp(Rd)),方程(2)在Lp(0,T;Lp(Rd))的意义下,有且仅有一个解h(x,t)满足h0(x)=0.进一步地,对所有的f∈Lp(0,T;Lp(Rd)存在一个只与p有关的正常数Cp,使得现在,应用最大Lp模正则性以及一些标准估计,我们得到了方程(1)弱解的先验估计：众所周知,弱解的L1模和L∞模有界是两个非常重要的性质.在进行先验估计的过程中,我们能够得到弱解的质量守恒.接下来,我们将应用Bootstrap迭代的方法证明弱解的L∞模是一致有界的.根据上面所得到的弱解的先验估计,我们能够通过构造(1)的正则化问题来证明方程弱解的全局存在性,即证明第二章的主要定理.我们考虑如下的正则化问题:对ε0,其中d≥3,0m2-2/d对初值u0ε(x)进行适当的假设,我们能够证明正则化问题存在一个经典解且满足定理0.0.1中所有的先验估计.在整个证明的过程中,我们主要遇到的困难是无法应用Aubin-Lions引理证明强收敛,因为只得到了的一致有界性而不是▽uε模的.因此,我们需要应用Aubin-Lions-Dubinskii引理[3]:引理0.0.2.设B,Y是Banach空间,M+是B中的一个非负半赋范锥,且满足M+∩Y≠(?),1≤p≤∞.如果(i)M+→B是紧的,(ii)对所有(ωn)(?)B,当n→∞时,在B中有ωn→ω,在Y中有ωn→0,则ω=0,(iii)U(?)Lp(0,T;M+∩Y)且在Lp(0,T;M+)中有界,(ⅳ)当h→0时,在u∈U中一致地有||u(t+h-h)-u(t)||Lp(0,T-h;Y)→0,那么U在Lp(0,T;B)中是相对紧的.为了应用Aubin-Lions-Dubinskii引理,我们选取B=Lp(Ω),并构造是一个满足下面定义的Lp+1中的非负半赋范锥.定义0.0.2.设B是一个Banach空间,M+(?)B满足(1)对所有的u∈M+,C≥0有有Cu∈M+,(2)存在函数[·]:M+→[0,∞),使得当且仅当u=0时,[u]=0,(3)对所有C≥0,有[Cu]=C[u],那么M+是B中的一个非负半赋范锥.从而,应用Aubin-Lions-Dubinskii引理,我们可以逐步的证明全局弱解的存在性.此外,当1m2-2/d时,弱解还是一个弱熵解.我们已经列出了证明第二章中存在性定理的重要思想,现在我们给出定理的完整叙述:在第二章的最后,我们证明了弱解的局部存在性并给出了一个爆破准则.当0m2-2/d时,退化抛物-抛物Keller-Segel方程弱解的有限时间爆破仍然是一个公开问题.第三章,我们在d≥3的情况下提出了p-LaplaceKeller-Segel方程:其中p1.这个模型是退化抛物-椭圆Keller-Segel模型的一个自然延伸,因为多孔介质方程和p-Laplace方程都叫作非线性扩散方程.二者虽然属于不同的领域,但在描述的现象上,使用的技巧上以及获得的结果上都有很多重合之处.在这个p-LaplaceKeller-Segel方程中,我们找到了一个临界指数p,它与方程(1)中的m=2-2/d扮演相同的角色.当p=3d/d+1时,如果(u,v)是方程(5)的一个解,我们构造u的质量守恒坐标变换以及相应的v的坐标变换那么(uλ,vλ)也是方程(5)的一个解.因此,我们将p=3d/d+1称为临界指数.对一般的p,(u λ,vλ)满足如下的方程根据p的不同取值,我们将问题分为超临界情形和次临界情形.当1p3d/d+1时,我们称为超临界情形.在超临界问题中,当细菌密度很高时,聚合作用强于扩散作用,导致有限时间爆破;当细菌密度很低时,扩散作用强于聚合作用,导致无限时间的传播.相应地,当p3d/d+1时,我们称为次临界情形.在次临界问题中,当细菌密度很高时,扩散作用强于聚合作用,阻止了有限时间爆破;当细菌密度很低时,聚合作用强于扩散作用,从而阻止了无限时间的传播.在第三章中,我们的主要目的是在超临界大初值假设下,证明方程(5)弱解的全局存在性.为了证明定理,我们首先要进行先验估计:对于p-LaplaceKeller-Segel方程,我们并没有像第二章一样得到u的质量守恒,这是一个公开问题.但是使用Bootstrap迭代方法,我们同样能够得到方程(5)弱解的L∞一致有界性.证明过程中的主要思想与定理0.0.2基本相同,但细节上却存在很大差异.得到弱解的先验估计后,我们构造方程(5)对应的正则化问题来证明本章中最主要的存在性定理:对于ε0这里α(d)是d-维单位球的体积.对初值u0ε(x)进行适当的假设,我们能够证明正则化问题存在一个经典解且满足定理0.0.4中所有的先验估计.那么结合Aubin-Lion引理得到的强收敛以及一致有界估计得到的弱收敛,我们能够证明第三章的主要定理:定理0.06.设d≥3,1p3d/d+1,q=d(3-p)/p.如果u0∈L+1(Rd)∩L ∞(Rd),A(d,p)=Cp,d3-p-‖u0‖Lq3-p0,其中Cp,d=[qpp/Kp(d,p)(q-2)+p)p]1/3-p是一个常数,那么方程(5)存在一个非负的全局弱解(u,v),使得定理0.04中所有的先验估计以及定理0.05中的L∞一致有界估计都成立.定理的证明过程中,困难的部分是用单调算子理论得到非线性项的极限.下面的引理是单调算子的一个重要性质:引理0.0.3.对任意η,η'∈Rd,下列不等式成立其中C1和和C2是两个只依赖于p的正数.当1p3d/d+1时,p-LaplaceKeller-Segel方程弱解的有限时间爆破仍然是有待解决的问题。
Empirical likelihood
统计和统计数据收集
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普遍调查实例
【例1.1】 2002年在国务院统一部署下，开展全国“基本 单位普查”。关于这次普查的部分重要要求与规定如下： 调查目的：统计分析全国和各省市地区的单位总数、性质、 隶属关系、分布情况等。 标准时间：2001年12月31日。 调查对象：各类法人单位，各类法人单位所属的产业活动 单位。 调查项目：单位总数；
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七.网上调查
截至 2009 年 6 月底，中国网民规模达到 3.38 亿 人 ， 较 2008 年 底 增 长 13.4% ， 上 网 普 及 率 达 到 25.5%。网民规模持续扩大，互联网普及率平稳上 升。其中宽带网民数达到3.2亿，占比高达94.3%， 较 2008 年底上升了 3.7 个百分点。另外，截至 2009 年 6 月底，作为国家域名， CN 域名总计达到 1,296 万个。作为我国互联网的重要基础资源，CN域名 已经广泛地应用在金融、汽车等各个行业中。截 止2009年6月我国互联网用户发展情况如图1.2所示。
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四.典型调查
——也是专门组织的一种非全面调查，在总体中选择 有代表性的典型单位进行深入细致的调查。 典型调查的作用和目的 (1) 研究新事物或某种倾向性的社会问题 通过对典型单位深入细致的调查，可以发现新情况、新问 题，探测事物发展变化的趋势，形成科学的预见。 (2) 分析事物的不同类型 通过研究造成它们间差别的原因，总结经验教训，研究对 策，促进事物的转化和发展。 (3) 典型调查可用来研究事务的变化规律。 (4) 典型调查的资料可用来补充和验证全面统计的数字，推论 和测算有关现象的总体。
统计数据的收集是统计整理和分析，以及统计 推断和预测的基础。社会经济统计中所需要的数据 与资料主要来源于统计调查。 统计数据的收集就是根据统计研究的目的和要 求，有组织、有计划地向调查对象搜集原始资料的 过程。 确定数据最合适的来源和收集数据的合理方法 是非常重要的任务，因为如果收集的数据有偏差， 模糊不清或有其他类型的错误时，即使最复杂的统 计方法也无法得到有用的信息，即需要避免 “Garbage In Garbage Out(垃圾数据产生垃圾统计结 果)”的统计应用情况。
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CHAPTER 1WHAT IS STATISTICSSECTIONS 1 - 4MULTIPLE CHOICE QUESTIONSIn the following multiple-choice questions, please circle the correct answer.1. You asked five of your classmates about their height. On the basis ofthis information, you stated that the average height of all students in your university or college is 65 inches. This is an example of:a.descriptive statisticsb.statistical inferencec.parameterd.populationANSWER: b2. A company has developed a new computer sound card, but the averagelifetime is unknown. In order to estimate this average, 200 sound cards are randomly selected from a large production line and tested and the average lifetime is found to be 5 years. The 200 sound cards represent the:a.parameterb.statisticc.sampled.populationANSWER: c3. A summary measure that is computed from a sample to describe acharacteristic of the population is called aa.parameterb.statisticc.populationd.sampleANSWER: b4. A summary measure that is computed from a population is called aa.parameterb.statisticc.populationd.sampleANSWER: a5. When data are collected in a statistical study for only a portion orsubset of all elements of interest, we are using a:a.sampleb.parameterc.populationd.statisticANSWER: a6. Which of the following is not the goal of descriptive statisticsa.Summarizing datab.Displaying aspects of the collected datac.Reporting numerical findingsd.Estimating characteristics of the populationANSWER: d7. Which of the following statements is not truea.One form of descriptive statistics uses graphical techniquesb.One form of descriptive statistics uses numerical techniquesc.In the language of statistics, population refers to a group of peopled.Statistical inference is used to draw conclusions or inferences aboutcharacteristics of populations based on sample dataANSWER: c8. Descriptive statistics deals with methods of:anizing datab.summarizing datac.presenting data in a convenient and informative wayd.All of the aboveANSWER: d9. A politician who is running for the office of governor of a state with 4million registered voters commissions a survey. In the survey, 54% of the 5,000 registered voters interviewed say they plan to vote for her.The population of interest is the:a. 4 million registered voters in the stateb.5,000 registered voters interviewedc.2,700 voters interviewed who plan to vote for her.d.2,300 voters interviewed who plan not to vote for herANSWER: a10. A company has developed a new battery, but the average lifetime isunknown. In order to estimate this average, a sample of 500 batteries is tested and the average lifetime of this sample is found to be 225 hours.The 225 hours is the value of a:a.parameterb.statisticc.sampled.populationANSWER: b11. The process of using sample statistics to draw conclusions about truepopulation parameters is calleda.inferential statisticsb.the scientific methodc.sampling methodd.descriptive statisticsANSWER: a12. Which of the following is most likely a population as opposed to asamplea.Respondents to a magazine surveyb.The first 10 students completing a final examc.Every fifth student to arrive at the book store on your campusd.Registered voters in the State of MichiganANSWER: d13. Researchers suspect that the average number of credits earned persemester by college students is rising. A researcher at Michigan State University (MSU) wished to estimate the number of credits earned by students during the fall semester of 2003 at MSU. To do so, he randomly selects 500 student transcripts and records the number of credits each student earned in the fall term 2003. He found that the average number of semester credits completed was credits per student. The population of interest to the researcher isa.all MSU studentsb.all college students in Michiganc.all MSU students enrolled in the fall semester of 2003d.all college students in Michigan enrolled in the fall semester of2003ANSWER: c14. The collection and summarization of the graduate degrees and researchareas of interest of the faculty in the University of Michigan of a particular academic institution is an example ofa.inferential statisticsb.descriptive statisticsc. a parameterd. a statisticANSWER: b15. Those methods involving the collection, presentation, andcharacterization of a set of data in order to properly describe the various features of that set of data are calleda.inferential statisticsb.the scientific methodc.sampling methodd.descriptive statisticsANSWER: d16. Which of the following is most likely a parameter as opposed to astatistica.The average score of the first ten students completing an assignmentb.The proportion of females registered to vote in Kent County, Michiganc.The average height of 100 students randomly selected from a communitycolleged.The proportion of cars stopped yesterday on US 131 that were citedfor speedingANSWER: b17. A study is under way in a national forest to determine the adult heightof pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 50 feet tall. It is estimated that the forest contains 32,000 pine trees. The study involves collecting heights from 500 randomly selected adult pine trees and analyzing the results. The sample in the study isa.the 500 randomly selected adult pine treesb.the 32,000 adult pine trees in the forestc.all the adult pine trees taller than 50 feetd.all pine trees, of any age in the forestANSWER: a18. The estimation of the population average student expenditure oneducation based on the sample average expenditure of 1,000 students isan example ofa.inferential statisticsb.descriptive statisticsc. a parameterd. a statisticANSWER: aTRUE / FALSE QUESTIONS19. When the purpose of the statistical inference is to draw a conclusionabout a population, the significance level, as a measure of reliability, measures how frequently the conclusion will be correct in the long run.ANSWER: F20. A summary measure that is computed from a sample to describe acharacteristic of the population is called a statistic.ANSWER: T21. The confidence level is the proportion of times that an estimatingprocedure will be wrong.ANSWER: F22. Conclusions and estimates about a population based on sample data arenot always going to be correct. For this reason measures of reliability, such as the significance level and the confidence level, should be built into the statistical inference.ANSWER: T23. A university employs 2500 faculty and staff. To ascertain how theemployees feel regarding a health insurance plan, 250 of the employees are surveyed. The proportion of the 250 employees who favor the health insurance plan is a parameter.ANSWER: F24. In a sample of 400 students in a college of business, 120 of them or 30%are marketing majors. The 30% is an example of statistical inference as opposed to descriptive statistics.ANSWER: F25. Twenty-five percent of a sample of 200 tennis players indicated thattheir parents did not play tennis. Based on this sample, we estimate that the 25% figure holds for the parents of all professional tennis players. This is an example of descriptive statistics as opposed to statistical inference.ANSWER: F26. A population is the totality of items or things of interest underconsideration.ANSWER: T27. A local cable system using a sample of 800 subscribers estimates thatforty percent of its subscribers watch premium channel at most four times a week. This is an example of statistical inference as opposed to descriptive statisticsANSWER: T28. A statistic is usually unobservable while a parameter is usuallyobservable.ANSWER: F29. Statistical inference is the process of making an estimate, prediction,or decision about a population based on sample data.ANSWER: T30. A summary measure that is computed from a population is called aparameter.ANSWER: T31. A sample is the portion of the universe that is selected for analysisand making inferences about the population from which the sample is selected.ANSWER: T32. As a population becomes large, it is usually better to obtainstatistical information from the entire population.ANSWER: F33. A statistic is usually used to provide an estimate for a usuallyunobserved parameter.ANSWER: T34. A sample is always a good representation of the target population.ANSWER: F35. Estimating characteristics of the population is the main goal ofdescriptive statistics.ANSWER: FSTATISTICAL CONCEPTS & APPLIED QUESTIONS36. In statistics, what name do we give to a numerical characteristic of asampleANSWER:Statistic37. In statistics, what name do we give to a numerical characteristic of apopulationANSWER:Parameter38. A manufacturer of children toys claims that less than 3% of his productsare defective. When 500 toys were drawn from a large production run, 5% were found to be defective.a.What is the population of interestb.What is the samplec.What is the parameterd.What is the statistice.Does the value 3% refer to the parameter or the statistic Whyf.Does the value 5% refer to the parameter or the statistic Whyg.Explain briefly how the statistic can be used to make inferencesabout the parameter to test the claim.ANSWER:a.The complete production run of toysb.The 500 toys drawn from the production runc.Proportion of the production run toys that are defectived.Proportion of sample toys that are defectivee.Parameter; since it is a summary measure that is computed from thepopulationf.Statistic; since it is a summary measure that is computed from thesampleg.Since the sample proportion is more than 3%, we conclude that theclaim is false.39. The Human Resources Director of a large insurance company wishes todevelop an employee health benefits package and decides to select 400 employees from a list of employees in order to study their preferences for the various components of a potential package. The 400 employees who will participate in this study constitute the __________.ANSWER:sample40. The Human Resources Director of a large hospital in California wishes todevelop an employee health benefits package and decides to select 300 employees from a list of all employees in order to study their preferences for the various components of a potential package.Information obtained from the sample will be used to draw conclusions about the true population __________.ANSWER:parameters41. The Commissioner of Health in California State wanted to studymalpractice litigation in Los Angeles. A sample of 32,000 medical records was drawn from a population of million patients who were discharged during the year 2003. Using the information obtained from the sample to predict population characteristics with respect to malpractice litigation is an example of __________.ANSWER:inferential statistics42. The Human Resources Director of a large automobile corporation inMichigan wishes to develop an employee pension package and decides to select 500 employees from a list of all auto workers in order to study their preference for the various components of a potential package. In this study, methods that result in decisions concerning population characteristics based only on the sample results are called __________.ANSWER:inferential statistics43. The Commissioner of Health in California State wanted to studymalpractice litigation in Los Angeles. A sample of 32,000 medicalrecords was drawn from a population of million patients who were discharged during the year 2003. The true proportion of malpractice claims filed from the population of million patients is a __________.ANSWER:parameter44. A businessman who is running for the vacant City Mayor seat with 25,000registered voters conducts a survey. In the survey, 55% of the 500 registered voters interviewed say they planned to vote for him.a.What is the population of interestb.What is the samplec.Is the 55% a parameter or a statistic WhyANSWER:a.The political choices of the 25,000 registered voters.b.The political choices of the 500 registered voters interviewed.c.Statistic; since it is a summary measure that is computed from thesample45. Define each of the following statistical terms:a.Descriptive statisticsb.Statistical inferencec.Confidence leveld.Significance levele.Populationf.SampleANSWER:a.Descriptive statistics deals with methods of organizing, summarizing,and presenting data in a convenient and informative way.b. Statistical inference is the process of making estimate, prediction,or decision about a population based on sample data.c.The confidence level is a measure of reliability that measures theproportion of times that an estimating procedure will be correct.d.The significance level is a measure of reliability that measures howfrequently the conclusion about a population will be wrong in thelong run.e. A population is the group of all items of interest to a statisticspractitioner. It is frequently very large and may, in fact, beinfinitely large.f. A sample is a set of data drawn from the population.46. Identify each of the following studies as either descriptive statisticsor statistical inference.a.Examine the weights of a sample of 75 manufacturer parts to see ifthe average weight of all the parts produced by the process is 2pounds.b.Post the average final score for your statistics class.c.Estimate the percentage of the US population that will vote for JohnKerry in the 2004 presidential election.d.Select a random sample of 100 babies born in 2003 and estimate thebirth weight of all babies born during the same year.e.Examine the weights of a sample of 10 cans of corn to see if theiraverage weight is 16 ounces.ANSWER:a.Statistical inferenceb.Descriptive statisticsc.Statistical inferenced.Statistical inferencee.Descriptive statistics47. The Commissioner of Health in California State wanted to studymalpractice litigation in Los Angeles. A sample of 32,000 medical records was drawn from a population of million patients who were discharged during the year 2003. The collection, presentation, and characterization of the data from patient medical records are examples of __________.ANSWER:descriptive statistics48. The Human Resources Director of a large automobile corporation inMichigan wishes to develop an employee pension package and decides to select 500 employees from a list of all auto workers in order to study their preferences for the various components of a potential package. Inthis study, methods involving the collection, presentation, and characterization of the data are called __________.ANSWER:descriptive statistics49. The Commissioner of Health in California State wanted to studymalpractice litigation in Los Angeles. A sample of 30,000 medical records was drawn from a population of million patients who were discharged during the year 2003. The proportion of malpractice claims filed from the 32,000 patients is a __________.ANSWER:statistic50. The Human Resources Director at Michigan State University wishes todevelop an employee benefits package and decides to select 500 employees from a list of all employees in order to study their preferences for the various components of a potential package. The Director will use the data from the sample to compute __________.ANSWER:statistics51. The Human Resources Director at Florida State University wishes todevelop an employee benefits package and decides to select 200 employees from a list of employees in order to study their preferences for thevarious components of a potential package. All the employees in the university constitute the __________.ANSWER:population52. At Grand Rapids Community College 150 students are randomly selected andasked the distance of their commute to campus. From this group a mean of miles is computed.a.What is the parameterb.What is the statisticsc.What is the populationd.What is the sampleANSWER:a.The mean commute distance for all students at the collegeb.The computed milesc.All students enrolled at the colleged.The 150 randomly selected students53. Consider the population of all tennis players in the world. Define fivesamples that can be taken from this population.ANSWER:US tennis players, Female tennis players, Left-handed tennis players, Pro tennis players, and European tennis players who won US open54. An office supply warehouse has boxes of pencils, 100 pencils to the box.Information about the entire warehouse as well as a sample of the boxes is shown below:a.What is the value of the statisticb.What is the value of the parameterANSWER:a.6b.7055. Briefly describe the difference between parameter and statistic, andgive an example of each.ANSWER:A parameter is a descriptive measure of a population.Example: The mean number of soft drinks consumed by all students at the University of Michigan.A statistics is a descriptive measure of a sampleExample: The mean number of soft drinks consumed last week by a sample of 250 students from the University of Michigan.。