周五晚上下班后，在网上胡乱搜索了一些关键词，找到了应届生这个论坛。看起来上面的网友还是挺活跃的，我下载了一些 verbal 和 numerical 的练习。没想到第一个关于inflation的题就把我卡住了，找到邻居一个学finance的小弟帮忙，事后证明我又一次愚蠢地把简单问题复杂化，建议没考的朋友们一定不要把题目看得太难。

周六早晨赖床到10点，吃了点午饭就去笔试，笔试前在图书馆还小复习了一下之前看的材料。网上多数笔经是中文的，但 consulting 的笔试为全英文，也许这样避免了看那些翻译的很拗口的中文句子，仁者见仁。随后去笔试，进入系统后发现考试分为3个部分，verbal, numerical 和 logical，分别有2道大题，每个大题3个问题，另外每个大题有3分钟时间完成，如果时间耗尽将自动进入下一题，在每个大题回答的过程中可以任意地根据题号跳到不同的小问题上，所以点 next 之后不必紧张。

verbal reasoning 首先开始，第一篇题干大意是说电脑病毒如今已不再依赖邮件，而是通过下载来传播，其中介绍了少数黑客通过破坏手段进行的犯罪行为。之后说随着病毒的增加，一些信息安全公司开始开发一些补丁来应对漏洞。题目似乎很容易，因为文章逻辑清晰没有什么难点，答题注意细节就好。第二篇我觉得对文章把握的不是很好，好像是在说对员工培训的一种方法，题目机会均为细节题，得认真从文章里比较，其中有个考察词汇的题目我记得是用 widespread 替换 pervasive 木有难度。但是那几道细节真的找的我疯了，好久没看过雅思对 F 和 NA 把握的能力也不太好，最后一题随便填了一个时间就到了，感觉真的是压力测试啊，一慌就完了。

下面开始测试 numerical，这个貌似没有什么难度，也没发现陷阱，拿好计算器别按错了就行了。

最后一部分为 logical，考前我竟然不知道，也从没做过类似的题目，就是几个图形通过一种变换成为另外的几个图形，其实这种题本身难度不大，但由于我没有把关键的信息写到纸上，以至于看到第4问的时候就有点把运算关系搞混了，重新来推时间已然来不及，貌似蒙了3个小题，这个部分很失败。建议考 consulting 的同学一定做笔记啊！

就这样考完了回家路上拍了张照片，攒rp的同时也祝你们好运吧！

9月底，由于 China Entrepreneur Network Cornell chapter 举办了 Annual Forum，我们一行7人驱车赶去参加。记得那是我极其忙碌的一周，周三先乘火车去 chicago 参加了 BCG 大中华的 recruiting，次日凌晨才赶回学校。第二天下午就又冒着大雨向 Cornell 前行。

Cornell University 不愧是常春藤盟校，处处都透着学术的气息，我在论坛的第一天遇到了刚从图书馆学习完赶过来的小学妹，刚刚入学身上已经沾满的康奈尔人特有的精神。再图书馆工作的她给我介绍了学校图书馆的概况，也为我们第二天的图书馆之旅奠定了基础。我还认识了一个来自亚利桑那 Thunderbird 全球管理学院的姐姐，听她说话字里行间都透漏着 professional，但我并没有听过她的学校，但是心里甚至还不健康地把人小觑了一番，后来在 google 发现这所学校的全球管理专业竟然是全球第一的，而她就是这个专业快毕业的学生……

副校长致开幕词

论坛总是牛人出没，我还见到了一个想带美国人去中国了解文化的东北姑娘，一个想做 consulting 的双学位美国人，工作5年来 Cornell 镀金的日本人。第一天论坛最吸引我的地方就在于参与者并不是单纯地听讲座，而是得到了很多机会与嘉宾交流，互动，讨论甚至辩论，到了这个环节我的英语就有点跟不上了，很多想到的观点找不到合适的方式表达，看着有些同学能够和嘉宾各执一词，清晰地阐明自己的观点心中还是暗暗叹服。

雨滴下的 Cornell University

由于考试临近，我没参加第二天下午的论坛，中午吃过免费的午餐后就跑去康奈尔的图书馆自习。与其说是自习，其实我更是想看看名校的图书馆什么样的，这是个有名校情节的人必有得行为吧。

这里是 Uris Library,你有没有被震撼到呀？从没想想过图书馆可以这样的充满美感，多么向往自己能在里面待几年啊……

身处其中，实在陶醉

继续在这知识的迷雾中回荡

红红的地毯多么诱人，猜猜我是谁？

论坛结束后，我们的合照

晚上我们跑到康奈尔的 phd 学姐们的家里 party，开了两桌 Texas hold’em。来来去去手中的筹码就已然不多了，心理战在这里似乎超过了运气。U of M 的同学醉后还献歌几首，场面一度很 high。聊天，喝酒，那一刻所有人都那么真实简单，有一拿不到 phd 学位的大哥给我倾诉心中的苦闷，一个和我来自同一个城市的 phd 学姐深刻地告诫我们要慎重考虑未来的路，尤其是到底读不读 phd，我还和东北大妞讨论了在中国创业的事，也有的人睡着了…

那晚我们送一女生到宿舍时已经凌晨4点了，在宿舍楼前的草坪上，我看到几只小鹿若隐若现，太神奇了如仙境一般。第二日，我们一堆人睡到下午才醒，甚至超过了 check out 的时限。

归途

As behavior influence the result of this story, I decide to start from this point and find how it was affected. Lewin’s Equation,

B = f (P, E)

(B – Behavior; f – Function; P – Person; E – Environment)

is a psychological equation of behavior developed by Kurt Lewin. It states that behavior is a function of the person and his or her environment. Personality traits are the internal affection and environment is the external influence. In contemporary psychology, the “Big Five” factors are five broad domains of personality. In this paper, I will focus on three of them and analyze how they affect the behaviors of Koro and Paikea.

Openness is the quality of being open. If someone is open, he or she is easy to accept know perspectives and new ideas. Koro is a person who isn’t open, even though he is the chief of his tribe. He followed the traditional rule of Maori all his life, which brought too much burden for him and harmed those people around him. When his daughter-in-law was dead in childbirth, Koro didn’t even look at her and then he asked his son to come home and start again. He prayed for his dead grandson whereas he didn’t care about his live granddaughter. From the film, we know he isn’t an inexorable man; however, these details show that tradition and the responsibility of chief play crucial roles in his mind. He also loved his granddaughter, but when he became angry, he could say Pai is nothing to him which is the first thing in his mind. In his mind, choosing the next chief for the tribe is the most significant thing. Koro quarreled with his son Porourangi and said the artifacts his son made were just souvenirs. He is not open with his son’s career and interest, and everything conflicted with his mind must be wrong.

On the other side, Paikea is an open person. Even though she was grown up in Maori tribe, she was quite different from other women. When her grandpa Koro started the custom school and refused her, she never gave up and tried every opportunity to learn like other boys. She thought male and female should be treated equally, and women should also have chances to be a chief. In order to learn the tool fighting skill she asked her uncle for help. She beat the boy who learned it from his grandpa because the open thought was always in her mind. Everything she did broke the traditional rule but she did everything correct. It’s not only because of her fortune but also because of her persistent openness.

Agreeable is anther trait of the big five personality which is a tendency to be pleasant and accommodating in social situations. I don’t think Koro is agreeable because he always shows us the cold side of him. Porourangi is the first-born children and he is also a born artist. His sensitive and vulnerable characters made him hardly bore the severe requirements of being a chief. Koro never tried to understand Porourangi’s mind but force him to be a successor. Koro’s second son Rawiri is someone we shouldn’t neglect. He is a talented leader and he showed his leadership of being a chief in the last part of the movie when they were saving whales. He allocated assignments, encouraged people, and comforted others but reason he cannot be a chief is just he isn’t first-born. Koro never thought about how Rawiri’s feeling was that a man has everything to be a leader but can’t be. From Porourangi, Rawiri to Paikea, they were all Koro’s family members whereas Koro didn’t know their characters and he seldom concerned their feelings.

Compared with her grandpa, Paikea is an agreeable girl. Paikea is a girl who cannot become a chief in traditional rules but she was like a boy when we look at her personalities. She was more eager than those boys to learn custom songs and skills and she performed perfectly and each field. She was treated unequally since she was born. She avoided confrontation as much as possible with Koro; she wanted to say sorry to her grandpa; she never complained anything about herself or Koro; she respected to the tradition and accepted them; she understood her grandpa Koro and forgave him. She concerned a lot about Koro. She said in the speech that she came from a long line of chiefs. She was trying to find a new way to solve this problem.

Then I will talk about neuroticism. Neuroticism is a fundamental personality trait. It is an enduring tendency to experience negative emotional states. Neuroticism people are more likely to experience such feelings as anxiety, anger, guilt, and depressed mood. There is no denying that Koro is this type of people. He obeyed those rules and forced others to do that. In everybody’s eyes, he was a leader and a chief but he was cold to them. He was easy to be angry with each one who didn’t obey his law. He was also lonely. He locked himself into his narrow world and can’t get out. When no one brought his whale tooth back, he was sick and it was too difficult for him to recover. Somebody feels that his is happy because his standard is appropriate. Koro made such a difficult standard for him and the people around him, so ha cannot be happy.

Personality traits affect people’s behaviors, while the environment also does. As the rule that only man can be a leader, it would be a big test for Paikea to become a chief. As Paikea was born in a chief family, it made her to determine to be a leader. Uncle Rawiri played an essential role of helping Paikea to be a chief. Without Rawiri, Paikea couldn’t learn how to fight with sticks; without Rawiri, she couldn’t know the place where Koro lost his whale tooth. If we consider carefully about here, we may know that the environment can change everything about a person.

In Lewin’s study, one’s behavior is determined by personalities and the environment around him or her. Paikea is an open and agreeable girl; meanwhile, the environment also brought either positive or negative influence for her behaviors. Koro isn’t open, agreeable and he cannot control his emotion. Most of the negative environments around him were made by himself but he some people like his wife and Paikea also brought him some positive effects. His wife knew it was impossible to change his mind, but helping him in some special situation was necessary. When Paikea rode the whale leaving, she gave the whale tooth to Koro.

When he knew that he didn’t have to blame anyone, he understand what life should be like; who should be the leader and he has built a new better tradition for Maori.

坐在夏威夷的一家咖啡馆里，一边咂摸着甜腻的咖啡，一边晒着窗外透进来的阳光，手里还不断地刷新着邮箱等待着需要的邮件和syllabus突然出现。

一路太过转辗，从家里匆匆忙忙赶到北京，机场的椅子甚至都没被我暖热就飞往首尔，身边坐了一个英国小伙，当他得知我转机去夏威夷时流露出满目的惊讶，却忘了他自己是转机去马代的。其实，又有谁知道我这分明是在绕路。人类不满足的进程和对别人羡慕的脚步永远无法停歇。B777宽敞的座椅至少还是令人愉悦的，1小时25分钟的行程很快就到了首尔仁川，那个硕大无比的航站楼。我在100多个登机口中搜寻着属于我的19号，可想而知那是多么艰难。一路的打折免税都已然无法吸引我的眼球（貌似平时也没法吸引我的眼球），跟着路标一刻不停。移动电话在韩国失效了，幸好还有免费wifi，还有人人网，还有新浪围脖能让我报个平安，也算这几个网站发挥着为数不多的作用。掏出登机牌才看到飞机莫名其妙地推迟了1小时，而我的电脑也莫名其妙地没电了，一切都充满奇妙，韩国我不得不说你是个奇妙的国度。从首尔到夏威夷的班机一直是我最喜爱的，为什么？宽敞的座椅，正常的食品，还配有独立的影视系统，以后需要增加的还有免费wifi和电源插口。然而，这班飞机最让我开心的并不是这些，而是飞机开始移动的时候我竟然发现了许多空位，我假装惊奇，“哇，有好多空位呀！”旁边的同学很自觉地搬到了后面，我一下拥有了两个人的座位，看了会电影以后我倒头睡到天亮，其实并不是天亮而是飞机开灯，因为当我打开遮光板一股强烈的宇宙射线刺入我的双目，哦，太阳已经升起来很久了。在夏威夷入境时，边检都不敢相信我选择这样的行程去上学，他一直好奇地问我今天准备去哪玩，但我身体的每个角落都告诉他我今天可玩不动了，需要休息，他竟然说去沙滩休息吧，这帮人每天真是工作乏味生活无聊，从绝望中寻找希望，他们都该去新东方。走出机场，一切欣欣向荣地冲我招手，但我似乎还是在半夜的状态，这就是时差，夏威夷也不例外。航站楼外没有wifi，航站楼外不提供软的休息座椅，公交车不让箱子上车，这里注定不是一个过客的居所。步行1000米找到一家咖啡馆开始了开头的一幕。

作为一个商界媒体的一面大旗，华尔街日报在美国甚至全球的有着巨大的影响力。我这个理工课学生所了解的为数不多的金融知识也都是从中所获。如臭名昭著网友一毛不拔所说，在华尔街日报上你找到到世间一切问题的答案，这句话一点也不夸张。看着身边不少同学省吃俭用夏天不舍得开空调冬天都不舍得开暖气只为省出200多刀订一年的华尔街日报，我被他们探求未知的精神不断打动，于是决定今天在这发布一个免费阅读华尔街日报的方法，希望可以帮助好学的你早日成为像一毛不拔一样的人。

1. 大家必须使用firefox浏览器，还在用IE,360的用户请自行更换。
2. 去firefox的官方插件站下载一个名字叫做refspoof的插件，安装，并重启firefox。
3. 在浏览器地址栏输入wsj.com来浏览华尔街日报的时候，同时在refspoof的工具栏的地址栏输入google.com，refspoof 工具栏的右侧选择static referrer（静止导入页）。继续浏览华尔街日报的页面你就会发现，那些之前需要付费的内容都可以直接阅读了。具体操作见下图：

华尔街日报作为默多克新闻集团旗下的媒体，也因此是少了几分内容免费的气度，毕竟这个为了进入美国市场而改了国籍的澳大利亚人对于Google和其带来的免费新闻搜索业务抢夺其传统媒体市场一直也是耿耿于怀。于是，华尔街日报的很多内容都是需要付费才可以浏览的。也正是因为这样，贫穷的我们开始了探索免费阅读华尔街日报的方法，而这方法中竟然还有Google的影子。

你肯定会问为什么要把导入地址设置成google.com呢？其实这个方法并不神奇，Google作为搜索引擎大亨就连默多克的华尔街日报也得屈服。为了增加搜索引擎的点击率也就是所谓的SEO，从而给记者们多赚点车马费，华尔街日报只能将后台所有来源于Google的请求开放。在这场默多克和Google的较量中，收益的还是我们这些贫穷的读者。

开学不久旧室友Danan送了我ipod touch2 MC系列，一直没顾上越狱所以只下载了一些免费的软件使用。仅仅一些免费软件再加上无线网络的支持就给我带来了很大的方便，我甚至一度用ipod看书而放弃了购买kindle，当然这无法代替。一晃而过，假期就这么朝我迎面扑来以至于我没做好任何准备，所以只能先继续住在学校里。这几天有大把时间所以我也顺便把ipod越狱。

午饭后，打开weiphone论坛随便搜索了几个帖子就开始了工作，原因很简单，我认为作为一个一年以前上市的电子产品，它的破解应该已然做了非常成熟了，并且我也非常相信网上这帮小白鼠的实验。然而，事情却并非如我最初的想象。

我按照帖子上的说法破解三遍后仍然失败。（破解这么多次其实主要是因为我一直在啃汉堡感觉自己手没有按紧Home键…）我重新阅读了帖子，发现ipod touch2竟然还有两个版本，一个叫做Non-MC，一个叫做MC。搜索之后发现MC是touch版本序号，Non-MC也就是MB。而我的就恰恰是MC系列的并且已经把固件升级到了4.2.1版本，所以完全不能用论坛上一般的帖子继续越狱了。

想到这里，我觉得自己还是太过心急，于是我放慢节奏重新开始了解关于ipod越狱的资料。由于硬件问题，MC系列ipod如果固件被不幸地升级到4.2.1以后目前还不能用主流的两种越狱方法实施。于是只能把升级后的操作系统降级。我参考了一些帖子关于iphone4操作系统降级的办法，终于把手里的ipod系统从4.2.1版本降回到4.1，降级方法如下：

1. 下载ipod touch2 MC的ios4.1升级包
2. 修改操作系统hosts文件，首先打开系统盘下X:\Windows\System32\drivers\etc\中修改hosts文件 (X为你的系统盘符）。编辑并添加以下内容于文件末尾：

74.208.10.249 gs.apple.com

74.208.105.171 gs.apple.com

保存后退出 ，win7用户要有管理员身份打开hosts。

3.进入DFU模式开始恢复，首先将ipod连接上PC，将ipod关机。然后按住开机键2秒不放，同时按住Home健数10秒后

松开开机键，继续按住Home键，直到ipod重新链接PC，USB+itunes时开始恢复 。

4.最后我们打开itunes，按键盘的Shift+恢复。现在就可以可以选择4.1的iOS进行升级了！

将ipod降级到4.1后，我们就可以安心地使用green poison 进行越狱了。

1. 下载 green poison 软件。Green poison 是Chronic Dev Team专门制作的一款破解apple系统的黑客工具。
2. 讲ipod插上数据线然后打开greenpois0n软件按中间的 Prepare to jailbreak! 按照提示时间操作进入DFU模式，方法如降级系统的第3步。
3. 进入DFU模式后，点击jailbreak开始越狱！工作结束后会自动退出Green poison并且自动重启ipod。
4. 重启后桌面上会出现一个load图标，先打开wifi 并确定可以连接上网再打开桌面上的load图标。选择并下载安装cydia，安装完成后卸载load返回会主菜单会自动重启，至此越狱完成。

正在越狱的ipod

上一张越狱成功后的图片，所有app都免费了，哈哈。

1.Hypergeometric random number X with parameter (n;M;N) has pmf

Write R function that will take input m and generate random number with Hypergeo-metric distribution with parameter (5, 7, 10), using inverse transformation method.

这个问题我纠结了很久，因为题目要求使用反函数法求解。显然，超几何分布的反函数这种变态东西不是我这个常人听说过的，说实话作为统计系的我甚至连超几何分布的 cdf 也不知道是什么……我尝试用 Mathematica 求解超几何分布 cdf 的反函数，结果失败，貌似 Mathematica 的符号运算不是很强大，听说 Maple 的符号运算很牛就独自跑到图书馆用免费的正版 Maple 算了一下午仍然没有什么好的结果。一气之下我上网搜索了一下关键词，竟然真的找到了…没错在这里，这个叫做Vose的网站是我目前见过的分析统计模型最完善的网站，虽然这个软件需要购买(这么牛的东西免费了开发者吃什么)，但数据库中提供的免费模型已经最够我们目前使用。我的第一次尝试就是把这些可恶的 Gamma 函数堆砌到自己的运算程序里，还不错很成功地把结果算出来了。

这件事没有这么过去，受暴风雪天气的影响全校停课一天，随之而来的各种课程取消，作业推迟提交的消息像雪片一样砸向我的邮箱。既然不急着交我就再考虑一下，心里总是觉得这个题的解法有点问题，毕竟让我们上网搜索一个 BT 公式不是教授出题的目的所在，那会是什么样呢？整个题目没有任何特殊之处，除了(5,7,10)这组给定数据。瞬时间，我似乎明白了问题的症结所在，n 是5说明参数 x 最大只能是5！所以这个问题其实是一个计算有限的离散点……很快把代码改好了，距离作业提交还有2天时间，不会的同学呢请光顾我的网站，但似乎他们找不到这，因为…他们几乎都是米国人。

## Main function ##
sampler <- function(m){
 n <- 5
 M <- 7
 N <- 10
 S <- 0
 rv <- NULL
 for (i in 1:m){
 x <- ceiling(runif(1,min=0,max=5))
 for (j in 1:x){
 X <- choose(M,x)*choose(N-M,n-x)/choose(N,x)
 S <- S + X
 j <- j + 1
 }
 rv <- c(rv,S)
 }
 return(rv)
}

hypergeo <- sampler(10000)

2.Let X be a random variable with pdf

and 0 otherwise. Write R function that will take imput n and generate random num-ber with above function using Inverse transformation method. Plot histogram of one realization with n = 1000 and overlay theoretical density function.

n <- 1000
 u <- runif(n)
 x <- 3*u^(1/4)
 hist(x, prob = TRUE)
 y <-  seq(0, 3, .01)
 lines(y,(y^3)*4/81, col="red")

3.Write R function that will take imput n and generate random number with distribution in the previous question using Acceptance-Rejection method. Plot empirical CDF of one realization with n = 1000 and overlay theoretical distribution function.

n <- 1000
 k <- 0
 j <- 0
 y <- numeric(n)

 while (k < n) {
 u <- runif(n,0,4/3)
 j <- j + 1
 x <- runif(n,0,3)
 if ( (x^3)*4/81 > u){
 k <- k + 1
 y[k] <- x
 }
}
 plot.ecdf(y)
 z <-  seq(0, 3, .01)
 lines(z,(z^4)/81, col="red")

]]> http://www.mathsoros.com/archives/1032/feed 7 http://www.mathsoros.com/archives/1028 http://www.mathsoros.com/archives/1028#comments Wed, 02 Feb 2011 05:36:33 +0000 mathsoros http://www.mathsoros.com/?p=1028

The New Boy

特别喜欢在寂静的夜晚，一个人坐在书桌前写点什么，写点什么都行。沉默之间，我与灵魂对话，一问一答，毫厘不差。

现在已是除夕，不论家乡还是我这。过往总是令人伤感，但很多人还没来得及想清楚所伤何物时间就已经把一切冲洗得干干净净。如果用曲线来拟合过去一年的我，那这张图似乎是非常曲折的，我历经了太多的转折。有的枪口转弯，有的甚至直接峰回路转，但这些就足以表达我的生活吗？有时候经历过的苦难更容易叫人忘却。

很感谢我的父母，每次在我遇到困难时都会尽力帮我想办法走出来，即使他们对那些领域非常未知仍然能耐下心来帮助我，每当这个时候我也都会鼓起勇气继续面对。今晚在电话中可以听到他们的些许无奈与苦楚，也只有这个时候人才能够理解团聚的意义。

上一个周末，我看完了第五遍电影《肖申克的救赎》，影片中的越狱给我暗示了无尽的希望。我也要逃离陈旧的生活，一直逃亡下去，追着地平线领跑，踏着满天星飞翔。对于那些由不得自己解决的困难，我将不再过问，新的一年最大限度地丰富经历，做好能做好的自己！最后把开头的歌曲送给大家当作新春的祝福：The New Boy

Google 最近推出了工具 Google NGram，利用它我们可以看到横跨500年超过500万本书籍中关键词的数量。非常有趣的统计工具，值得一试。

1.(a)Create vector s = (1; q; q2; : : : ; q50)T for q = 0.33

q <- .33

b <- 0:50   # line a <- rep(q,50) was irrerevant

s <- q^b

(b)Create vector t = (1; 4a; 7a; 10a; : : : ; 151a)T for a = 0.8

b <- seq(1,151,3)

a <- .8

t <- a*b

t[1] <- 1

(c)Create vector r = (1; 3b3; 3b5; 3b7; : : : ; 3b102)T for b = 0.43

a <- seq(1,101,2)

b <- .43

r <- 3*(b^a)

r[1] <- 1

(d)Dene a function named vec takes arbitrary value for b, and returns a vector r = (1; 3b3; 3b5; 3b7; : : : ; 3b102)T . Execute the function with b =0.55, and assign
the vector to X.

vec <- function(b){

a <- seq (1,101,2)

r <- 3*(b^a)

r[1] <- 1

return(r)

}

vec(.55)

(e)Calculate inner product (sT . t), and (tT . r).

s %*% t

t %*% r

2. From Class web page, download Lab1_sampleC.csv and Lab1_sampleD.txt.

(a)Read in the two files.

A <- read.table(file = “Lab1_sampleC.txt”, header = T)

B <- read.csv(file = “Lab1_sampleD.csv”, header = T)

(b)Merge two datasets.

X <- rbind (A,B)

(c)Sort the data according to the nal score.

ind <- unlist(sort( X$ Final, decreasing = T, index.return = T)[2])

Y <- X[ind,]

Y <- rbind(Y[-1,],Y[1,])   #put “Total” on the bottom

(d)For Midterm 1, obtain mean, and std dev.

mean(X$M1)

sd(X$M1)

(e)For Midterm 2, plot histgram of the scores.

hist(X$M2)

(f)Convert all the scores into percentages. the row \TOTAL” contains total points for each HW and Exams.

X.perc <- apply(X[,3:10], 1, function(a) a/unlist(X[37,3:10]))  # watch out that the result is transposed

X.perc <- round(X.perc,2)

X.perc <- cbind(X[,1:2],t(X.perc))   # X.perc had to be transposed back

(g)For each student, calculate the HW points by dropping the lowest HW (in %) and
averaging. Store the value in a new column called HWav.

X.perc$HWdrop <- apply(X.perc[,3:7], 1, function(x) (-1)*min(x) )  # gives value of min HW. 1 means do it by row

X.perc$HWav <- apply(cbind(X.perc[3:7],X.perc$HWdrop), 1, function(x)round(sum(x)/4, 2) )

# total of 5 HWs

(h)For each student, calculate course grade. by taking the average of four scores:HWav, M1, M2, and Final (in %).

X.perc$Course <- (X.perc$HWav+X.perc$M1+X.perc$M2+X.perc$Final)/4

ind <- unlist(sort(X.perc$Course, decreasing=T, index.return=T)[2])

X.perc <- X.perc[ind,]

X.perc <- rbind(X.perc[-1,],X.perc[1,])   #put “Total” on the bottom