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2016王式安概率论冲刺班讲义

2016王式安概率论冲刺班讲义
2016王式安概率论冲刺班讲义

《概率论与数理统计》讲义#(精选.)

第一章 随机事件和概率 第一节 基本概念 1、排列组合初步 (1)排列组合公式 )! (! n m m P n m -= 从m 个人中挑出n 个人进行排列的可能数。 )! (!! n m n m C n m -= 从m 个人中挑出n 个人进行组合的可能数。 例1.1:方程 x x x C C C 765107 11=-的解是 A . 4 B . 3 C . 2 D . 1 例1.2:有5个队伍参加了甲A 联赛,两两之间进行循环赛两场,试问总共的场次是多少? (2)加法原理(两种方法均能完成此事):m+n 某件事由两种方法来完成,第一种方法可由m 种方法完成,第二种方法可由n 种方法来完成,则这件事可由m+n 种方法来完成。 (3)乘法原理(两个步骤分别不能完成这件事):m ×n 某件事由两个步骤来完成,第一个步骤可由m 种方法完成,第二个步骤可由n 种方法来完成,则这件事可由m ×n 种方法来完成。 例1.3:从5位男同学和4位女同学中选出4位参加一个座谈会,要求与会成员中既有男同学又有女同学,有几种不同的选法? 例1.4:6张同排连号的电影票,分给3名男生和3名女生,如欲男女相间而坐,则不同的分法数为多少? 例1.5:用五种不同的颜色涂在右图中四个区域里,每一区域涂上一种颜

色,且相邻区域的颜色必须不同,则共有不同的涂法 A.120种B.140种 C.160种D.180种 (4)一些常见排列 ①特殊排列 ②相邻 ③彼此隔开 ④顺序一定和不可分辨 例1.6:晚会上有5个不同的唱歌节目和3个不同的舞蹈节目,问:分别按以下要求各可排出几种不同的节目单? ①3个舞蹈节目排在一起; ②3个舞蹈节目彼此隔开; ③3个舞蹈节目先后顺序一定。 例1.7:4幅大小不同的画,要求两幅最大的排在一起,问有多少种排法? 例1.8:5辆车排成1排,1辆黄色,1辆蓝色,3辆红色,且3辆红车不可分辨,问有多少种排法? ①重复排列和非重复排列(有序) 例1.9:5封不同的信,有6个信箱可供投递,共有多少种投信的方法? ②对立事件 例1.10:七人并坐,甲不坐首位,乙不坐末位,有几种不同的坐法? 例1.11:15人中取5人,有3个不能都取,有多少种取法? 例1.12:有4对人,组成一个3人小组,不能从任意一对中取2个,问有多少种可能性?

考研英语一新题型详解(跨考版)

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2016英语翻译考试资料

英语翻译考试资料 1、谦虚使人进步,骄傲使人落后。 Modesty helps one go forward ,whereas conceit makes one lag behind. 2、冬天来了,春天还会远吗? If winter comes,can spring be far behind? 3、人不犯我,我不犯人。 We will not attack unless we are attacked. 4、由于天气很好,我们决定去爬山。 As the weather was fine,we decided to clime the mountain. 5、没有外力的作用,运动的物体就保持匀速直线运动。 A body in motion remains at a constant speed in a straight line unless acted upon by an external force. 6、我们看见一只知更鸟,知道春天快要到了。 We knew spring was coming as we had seen a robin. 7、月球离地球非常遥远,即使那边山上长着大树,我们用已经发明的最高倍率的望远镜也不能看到他们。 The moon is so far from the earth that even if huge trees were growing on the mountains and elephants were walking about,we could not see them through the most powerful telescope which have been invented. 8、1826年杰文逊逝世。按他生前的遗愿,在他墓地的石碑上刻着:独立宣言和弗吉尼亚州信教自由法令的作者,弗吉尼亚大学创建人之墓。 Upon his death in 1826,Jefferson was buried under a stone which described him as he had wished to be remembered as the author of the Declaration on Independence and the Virginia Statute for Religious Freedom and the father of the University of Virginia. 9、我读过你的文章,但没料想到你会这样年轻。 I have read your articles,but I expect to meet an older man. 10、他们会冲着那从天际弯弯地挂向地面的,看起来好像伸手可及的美丽彩虹大声呼喊。 They would shout at the pretty rainbows that are down to the earth,seeming never very far away.

2007-2016考研英语新题型归纳总结(一)

2007-2016考研英语新题型归纳总结 (一) 考研英语新题型(七选五或排序题)虽然在分值中占比小,信息量大。但是在考研复习时,你仍然不能忽略它,阴沟里翻船的事常有,只有做好完全的准备,才能打赢考研这场持久战。今天小编为你汇总十年新题型词汇,希望对你复习新题型有所助益。 考研英语复习单词很重要,历年真题里出现的单词更是重要,最为重要。小伙伴们通常都是以四篇传统的大阅读为主要复习的重点,今天小编想送给各位考生的单词是大家容易忽略的一部分,历年真题新题型部分的单词,这一部分的单词也很关键,非常重要。 (一)2007年新题型词汇 Leisure 空闲的,休闲的 Collaborate 合作 figure out 弄清楚,理解 Authentic 真正的 transition 过渡 Clique 小圈子 Setback 挫折 Vaunted 大肆吹嘘的 start-up 开始阶段的 Foggy 朦胧的,模糊的 Unreadiness 未准备好的 Assign 分配 Periodically 定期地 Delay 延迟

Shortcomings 缺点Gratification 满足,满意Canned 录音的 Brainstorm 集思广益,风暴Passive 被动的,消极的Delicate 微妙的 Monotonous 单调的,枯燥的Fledgling 羽毛初长的雏鸟Stretch 一段时间 Naive 幼稚的 Bubble 泡沫,幻想 Conceive 构思 Endeavor 努力,尽力 Option 选择 Sustained 持续的 (二)2008年新题型词汇Draft 草稿 Substantiate 证明,证实Inevitable 不可避免的 Abrupt 突然的

概率统计讲义(教师版)

概率统计讲义 一.近5年全国卷高考题回顾 1.(2012?新课标 第11题) 将字母,,,,,a a b b c c 排成三行两列,要求每行的字母互不相同,每列的字母也互不相同,则不同的排列方法共有( ) (A )12种 (B )18种 (C )24种 (D )36种 2.(2012?新课标 第18题)某花店每天以每枝5元的价格从农场购进若干枝玫瑰花,然后以每枝10元的价格出售,如果当天卖不完,剩下的玫瑰花作垃圾处理. (1)若花店一天购进16枝玫瑰花,求当天的利润y (单位:元)关于当天需求量n (单位:枝,n ∈N )的函数解析式. 日需求量n 14 15 16 17 18 19 20 频数 10 20 16 16 15 13 10 (i )若花店一天购进16枝玫瑰花,X 表示当天的利润(单位:元),求X 的分布列,数学期望及方差; (ii )若花店计划一天购进16枝或17枝玫瑰花,你认为应购进16枝还是17枝?请说明理由. (1)当时, , 当 时, , 得:() *∈?? ?≥≤-=N n n n n y 16 ,8015 ,8010 (2)(ⅰ)X 可取60,70,80。 , X 的分布列为 , 。 (ⅱ)购进17枝时,当天的利润为76.4 > 76,从利润角度看,故应购进17枝。 而此时 ,说明购17支在利润相差不大的情况下,其波动较大,故购16支也可。 3.(2013 新课标 第3题)为了解某地区中小学生视力情况,拟从该地区的中小学生中抽取部分学生进行调查,事先已了解到该地区小学、初中、高中三个学段学生的视力情况有较大差异,而男女生视力情况差异不大,在下面的抽样方法中,最合理抽样方法是( ) A 、简单随机抽样 B 、按性别分层抽样 C 、按学段分层抽样 D 、系统抽样 4.(2013 新课标 第19题).一批产品需要进行质量检验,检验方案是:先从这批产品中任 取4件作检验,这4件产品中优质品的件数记为n 。如果n=3,再从这批产品中任取4件作

2016年12月英语四级翻译真题及参考答案

Part Ⅳ Translation (30 minutes) Directions: For this part, you are allowed 30 minutes to translate a passage from Chinese to English. You should write your answer on Answer Sheet 2. 2016年12月英语四级翻译真题及参考答案(卷一)红色 在中国文化中,红色通常象征着好运、长寿和幸福,在春节和其他喜庆场合,红色到处可见。人们把现金作为礼物送给家人或亲密朋友时,通常放在红信封里。红色在中国流行的另一个原因是人们把它与中国革命和共产党相联系。然而,红色并不总是代表好运与快乐。因为从前死者的名字常用红色书写,用红墨水写中国人名被看成是一种冒犯行为。 参考范文:

在中国文化中,黄颜色是一种很重要的颜色,因为它具有独特的象征意义。在封建(feudal)社会中,它象征统治者的权力和权威。那时,黄色是专为皇帝使用的颜色,皇家宫殿全都漆成黄色,皇袍总是黄色的,而普通老百姓是禁止穿黄色衣服的。在中国,黄色也是收获的象征。秋天庄稼成熟时,田野变得一片金黄。人们兴高采烈,庆祝丰收。 要点1:黄颜色是一种很重要的颜色yellow is an important color, 相信这句大家都能译的出来,不过要注意:“黄颜色”不需要写yellow color,因为yellow本来就是黄色。 要点2:它具有独特的象征意义which carries a unique symbolic meaning. 要点3:它象征着统治者的权利和权威It embodies rulers’ power and authority.此处,统治者可以接受的译法还有:governor, dominator 都是可以的。象征还可以写成symbolize,represent. 要点4:皇家宫殿全都漆成黄色royal palaces were painted with yellow. 皇家宫殿royal palaces,皇帝emperor,黄袍imperial robes. 要点5:普通老百姓是禁止穿黄色衣服的average people were not allowed to wear yellow clothes,禁止还可以用:ban, forbid. 要点6:秋天庄稼成熟时,田野变得一片金黄When crops are ripe in Fall,the farmlands become a piece of golden yellow.

12-16考研英语一新题型

16年 Part B Directions: In the following article, some sentences have been removed. For Questions 41-45, choose the most suitable one from the list A-G to fit into each of the numbered blank. There are two extra choices, which do not fit in any of the gaps. Mark your answers on ANSWER SHEET 1. (10 points) [A]Create a new image of yourself [B]Decide if the time is right [C]Have confidence in yourself [D]Understand the context [E]Work with professionals [F]Know your goals [G]Make it efficient No matter how formal or informa the work environment,the way you present yourself has an impact. This is especially true in first impressions. According to research from Princeton University,people assess your competence,trustworthiness,and likeability in just a tenth of a second,solely based on the way you look. The difference between today’s workplace and the“dress for success” era is that the range of options is so much broader. Norms have evolved and fragmented. In some settings, red sneakers or dress T-shirts can convey status; in others not so much. Plus, whatever image we present is magnified by social-media services like LinkedIn. Chances are, your headshots are seen much more often now than a decade or two ago. Millennials, it seems, face the paradox of being the least formal generation yet the most conscious of style and personal branding. It can be confusing. So how do we navigate this? How do we know when to invest in an upgrade? And what’s the best way to pull off one that enhance our goals? Here are some tips; 41. As an executive coach, I’ve seen image upgrades be particularly helpful during transitions---when looking for a new job, stepping into a new or more public role, or changing work environments. If you’re in a period of change or just feeling stuck and in a rut, now may be a good time. If you’re not sure, ask for honest feedback from trusted friends, colleagues and professionals. Look for cues about how others perceive you.Maybe there’s no need for an upgrade and that’s OK.

概率论基础讲义全

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不可能事件,以后 4、基本事件: 例如,在E1中,“掷出1点”,“掷出2点”,……,“掷出6点”均为此试验的基本事件。 例如,在E1中“掷出偶数点”便是复合事件。 5、样本空间:从集合观点看,常记为e. 例如,在E1中,用数字1,2,……,6表示掷出的点数,而由它们分别构成的单点集{1},{2},…{6}便是E1中的基本事件。在E2中,用H表示正面,T表示反面,此试验的样本点有(H,H),(H,T),(T,H),(T,T),其基本事件便是{(H,H)},{(H,T)},{(T,H)},{(T,T)}显然,任何事件均为某些样本点构成的集合。 例如,在E1中“掷出偶数点”的事件便可表为{2,4,6}。试验中所有样本点构成的集合称为样本空间。记为Ω。 例如, 在E1中,Ω={1,2,3,4,5,6} 在E2中,Ω={(H,H),(H,T),(T,H),(T,T)} 在E3中,Ω={0,1,2,……}

曹显兵.概率论讲义(打印版)

第一讲 随机事件与概率 考试要求 1. 了解样本空间的概念, 理解随机事件的概念, 掌握事件的关系与运算. 2. 理解概率、条件概率的概念, 掌握概率的基本性质, 会计算古典型概率和几何型概率, 掌握概率的加法公式、减法公式、乘法公式、全概率公式, 以及贝叶斯公式. 3. 理解事件独立性的概念, 掌握用事件独立性进行概率计算;理解独立重复试验的概率, 掌握计算有关事件概率的方法. 一、古典概型与几何概型 1.试验,样本空间与事件. 2.古典概型:设样本空间Ω为一个有限集,且每个样本点的出现具有等可能性,则 基本事件总数 中有利事件数 A A P = )( 3.几何概型:设Ω为欧氏空间中的一个有界区域, 样本点的出现具有等可能性,则 、体积)Ω的度量(长度、面积、体积)A的度量(长度、面积= )(A P 【例1】 一个盒中有4个黄球, 5个白球, 现按下列三种方式从中任取3个球, 试求取出的球中有2个黄球, 1 个白球的概率. (1) 一次取3个; (2) 一次取1 个, 取后不放回; (3) 一次取1个, 取后放回. 【例2 】从 (0,1) 中随机地取两个数,试求下列概率: (1) 两数之和小于1.2; (2) 两数之和小于1且其积小于 16 3. 一、 事件的关系与概率的性质 1. 事件之间的关系与运算律(与集合对应), 其中特别重要的关系有: (1) A 与B 互斥(互不相容) ? Φ=AB (2) A 与B 互逆(对立事件) ? Φ=AB , Ω=B A (3) A 与B 相互独立? P (AB )=P (A )P (B ). ? P (B|A )=P (B ) (P (A )>0). ?(|)(|)1P B A P B A += (0

0) ? 1)|()|(=+B A P B A P (0

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