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北京大学光华管理学院统计学四点攻克考博英语完形填空对于中国考生来说，虽然很多考生都已经通过了四级或者六级英语考试，但是对于英语能力的运用还不是很精通，考博英语也是同样如此，英语中的完形填空虽然已经伴随着我们走过了中学，大学，但是很多人还是对完形填空不能做到游刃有余，对于如何攻克这类问题，育明考博网校老师为各位提出以下几点建议，希望对考生有所帮助。
育明考博网校老师介绍，从大纲命题来看，考博英语完形填空从命题设置角度来看其实并不是很难。
因为，根据英语考博大纲来看，英语运用部分的阅读量并不大，字数一般在250-280字左右;而从文章以及其后每道题的选项设置上看，基本上考的是一些常规词，很难、很偏的词汇考到的几率非常低。
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根据命题规律，育明考博网校老师总结了一整套做英语完形的三种方法——逻辑关系法、非语法点排除法、全文对照法。
这套解题方法要求考生正确理解和把握完形填空文章的主题、整体结构布局、上下文语境和句子内部结构，训练考生从各个层次中定位未知填空的相关已知线索。
一、逻辑关系法考博试题的完型填空所选的文章都是具有逻辑关系、意义相连的语篇，而词语的重复出现、同义词和反义词的使用是重要的连句成篇的词汇组带。
因此，在行文中不可避免地会出现词语的复现、前后同义词、反义词相互照应等现象。
这就要求我们在做题的过程中，学会瞻前顾后。
此外，英语完形还有一类题是专门考察考生对于整篇短文的理解，如表明态度的选项，这就要求做题时，要把准文章的发展脉络，文章的起承转合，要注意段落与段落之间，句与句之间的内在逻辑关系，领悟暗示，选对答案。
二、排除非考语法点目前英语完形涉及语法的题目基本都不考时态、语态和虚拟语气。
那么，这样一来实际上剩下的语法已经不多了，句子结构、非谓语形式是关键，如否定倒装结构、强调句、主语从句等，提醒考生考试时一定要对此特别敏感，借助这些方面的语法知识，很多难题都会迎刃而解。
Problem Set21.Each time a shopper purchases a tube of toothpaste,he choose either brand A or brandthat he will chooseB.Suppose that for each purchase after thefirst,the probability is13that the same brand that he chose on his preceding purchase and the probability is23 he will switch brands.If he is equally likely to choose either brand A or brand B on hisfirst purchase,what is the probability that both hisfirst and second purchases will be brand A and both his third and fourth purchases will be brand B?2.In the World Series of baseball,two teams A and B play a sequence of games againsteach other,and thefirst team that wins a total of four games becomes the winner of the World series.If the probability that team A will win any particular game against team B is1/3,what is the probability that team A will win the World series?3.Suppose that A1,A2,...,A k are a sequence of k independent events.Let B1,B2,...,B kbe another sequence of k events such that for each value of j(j=1,2,...,k),either.Prove that B1,B2,...,B k are also independent events.Hint:B j=A j or B j=A Cj.Use an induction argument based on the number of events B j for which B j=A Cj4.Suppose that when a machine is adjusted properly,50percent of the items producedby it are of high quality and the other50percent are of medium quality.Suppose, however,that the machine is improperly adjusted during10percent of the time and that,under these conditions25percent of the items produced by it are of high quality and75percent are of medium quality.1)suppose thatfive items produced by the machine at a certain time are selected at random and inspected.If four of these items are of high quality and one item is of medium quality.What is the probability that the machine was adjusted properly at that time?2)Suppose that one additional item,which was produced by the machine at the same time as the otherfive items,is selected and found to be of medium quality.What is the new posterior probability that the machine was adjusted properly?。
Homework2光华管理学院概率统计作业Problem Set21.Each time a shopper purchases a tube of toothpaste,he choose either brand A or brandthat he will chooseB.Suppose that for each purchase after the?rst,the probability is13that the same brand that he chose on his preceding purchase and the probability is23 he will switch brands.If he is equally likely to choose either brand A or brand B on his?rst purchase,what is the probability that both his?rst and second purchases will be brand A and both his third and fourth purchases will be brand B?2.In the World Series of baseball,two teams A and B play a sequence of games againsteach other,and the?rst team that wins a total of four games becomes the winner of the World series.If the probability that team A will win any particular game against team B is1/3,what is the probability that team A will win the World series?3.Suppose that A1,A2,...,A k are a sequence of k independent events.Let B1,B2,...,B kbe another sequence of k events such that for each value of j(j=1,2,...,k),either.Prove that B1,B2,...,B k are also independent events.Hint:B j=A j or B j=A Cj.Use an induction argument based on the number of eventsB j for which B j=A Cj4.Suppose that when a machine is adjusted properly,50percent of the items producedby it are of high quality and the other50percent are of medium quality.Suppose, however,that the machine is improperly adjusted during10percent of the time and that,under these conditions25percent of the items produced by it are of high quality and75percent are of medium quality.1)suppose that?ve items produced by the machine at a certain time are selected at random and inspected.If four of these items are of high quality and one item is of medium quality.What is the probability that the machine was adjusted properly at that time?2)Suppose that one additional item,which was produced by the machine at the same time as the other?ve items,is selected and found to be of medium quality.What is the new posterior probability that the machine was adjusted properly?。
长春光华学院统计学原理期末专项B试卷学校___________ 班级_________ 姓名_________ 分数_________一、单项选择题（每小题1分共20分）1、在简单随机重复抽样情况下，若要求允许误差为原来的2／3，则样本容量( )A. 扩大为原来的3倍B. 扩大为原来的2／3倍C. 扩大为原来的4／9倍D.扩大为原来的2、数量指标指数和质量指标指数的划分依据是（）A：指数化指标的性质不同 B：所反映的对象范围不同C：所比较的现象特征不同 D：编制指数的方法不同3、对一批商品进行质量检验，最适宜采用的方法是（）A全面调查 B抽样调查 C典型调查 D重点调查4、抽样调查的目的在于（）。
A、了解总体的基本情况B、用样本指标推断总体指标C、对样本进行全面调查D、了解样本的基本情况5、下列分组中哪个是按品质标志分组（）。
A、企业按年生产能力分组B、产品按品种分组C、家庭按年收入水平分组D、人口按年龄分组6、加权算术平均数的大小受各组（）。
A、次数（f）的影响最大B、标志值（x）的影响最大C、权数（f/∑f）的影响最大D、标志值（x）和次数（f）的共同影响7、全面调查和非全面调查的划分依据是（）。
A、调查组织规模的大小B、调查对象所包括的单位是否完全C、最后取得的调查资料是否全面D、调查时间是否连续8、加权算术平均数的大小（）。
A、受各组次数的影响最大B、受各组标志值的影响最大C、受各组标志值和次数的共同影响D、不受各组次数的影响9、抽样推断的特点有（）。
A. 事先人为确定好样本B.按随机原则抽取样本C. 缺乏一定的科学性和可靠性D.事先无法计算和控制抽样误差10、两个相邻的定基发展速度相除等于（）A、环比发展速度B、定基增长速度C、环比增长速度D、定基发展速度11、某班学生的平均成绩是80分，标准差是5分。
如果已知该班学生的考试分数为对称分布，可以判断考试分数在70到90分之间的学生占( )A. 至少75%B. 大约68%C. 大约95%D. 大约99%12、对于不同水平的总体要比较其标志变动度，需分别计算各自的（）来比较。
《概率统计》作业本课程作业由二部分组成：第一部分为“客观题部分”，由15个选择题组成，每题1分，共15分； 第二部分为“主观题部分”，由4个解答题组成，第1、2题每题2.5分，第3、4题每题5分，共15分。
作业总分30分，将作为平时成绩记入课程总成绩。
客观题部分一、选择题（每题1分，共15分）1． A , B , C 三个事件中至少有两个事件，可表示为（ D ）A 、 ABCB 、ABC ABC ABC ++C 、 _______ABC D 、ABC ABC ABC ++2．设A , B , C 为任意三个事件，则_____________A B C ++=（ D ）A 、ABCB 、ABCC 、ABC ABC ABC ++D 、A B C ++3．设Ａ，Ｂ为任意两个事件，则（ A ）Ａ、()()()()P A B P A P B P AB +=+-Ｂ、()()()()P A B P A P B P AB -=--Ｃ、()()()()P A B P A P B P AB +=++Ｄ、()()()()P A B P A P B P AB -=-+4．设随机变量ξ服从参数为５的指数分布，则它的数学期望值为（ A ）Ａ５ Ｂ、15 Ｃ、２５ Ｄ、1255．设,[0,1],()0,[0,1].cx x p x x ∈⎧=⎨∉⎩若p(x)是一随机变量的概率密度函数，则c = ( C )A 、0B 、1C 、 2D 、36．设随机变量ξ服从参数为５的指数分布，则它的方差为（ A ）Ａ、125Ｂ、25 Ｃ、15 Ｄ、5 7．设A, B 为任意两个事件，则________A B +=（ B ）A 、AB B 、ABC 、A BD 、A B +8．设a <b , 则1,()b-a 0,a x b p x ⎧≤≤⎪=⎨⎪⎩其它是（ C ）分布的密度函数。
A 、指数B 、二项C 、均匀D 、泊松9．设总体Ｘ的均值μ与方差2σ都存在但均为未知参数，12,,,n X X X 为来自总体Ｘ的简单随机样本，记11ni i X X n ==∑，则μ的矩估计为（ A ） A 、X B 、1max{}i i n X ≤≤ C 、1min{}i i n X ≤≤ D 、2n 11(X )n i i X n =-∑ 10．已知事件A 与B 相互独立，且()P A B a ⋃=（a <1）,P (A )=b , 则P (B ) = ( A )A 、a-bB 、1-aC 、a b 1a-- D 、1-b 11．当ξ服从（ A ）分布时，必有E D ξξ=Ａ、指数 Ｂ、泊松 Ｃ、正态 Ｄ、均匀12．设123,,X X X 为来自正态总体(,1)N μ的容量为３的简单随机样本，则（ B ）是关于μ得最有效的无偏估计量。
概率论与数理统计习题及题解沈志军盛子宁第一章 概率论的基本概念1．设事件B A ,及B A 的概率分别为q p ,及r ，试求)(),(),(B A P B A P AB P 及)(AB P2．若C B A ,,相互独立，试证明：C B A ,,亦必相互独立。
3．试验E 为掷2颗骰子观察出现的点数。
每种结果以),(21x x 记之，其中21,x x 分别表示第一颗、第二颗骰子的点数。
设事件}10|),{(2121=+=x x x x A ， 事件}|),{(2121x x x x B >=。
试求)|(A B P 和)|(B A P4．某人有5把钥匙，但忘了开房门的是哪一把，只得逐把试开。
问：（1）恰好第三次打开房门锁的概率？（2）三次内打开的概率？（3）如果5把里有2把房门钥匙，则在三次内打开的概率又是多少？5．设有甲、乙两袋，甲袋中装有n 个白球、m 个红球，乙袋中装有N 个白球、M 个红球。
今从甲袋中任意取一个放入乙袋中，再从乙袋中任意取一个，问取到白球的概率是多少？6．在时间间隔5分钟内的任何时刻，两信号等可能地进入同一收音机，如果两信号进入收音机的间隔小于30秒，则收音机受到干扰。
试求收音机不受干扰的概率？7．甲、乙两船欲停靠同一码头，它们在一昼夜内独立地到达码头的时间是等可能的，各自在码头上停留的时间依次是1小时和2小时。
试求一船要等待空出码头的概率？8．某仓库同时装有甲、乙两种警报系统，每个系统单独使用的有效率分别为0.92,0.93,在甲系统失灵的条件下乙系统也失灵的概率为0.15。
试求下列事件的概率：（1）仓库发生意外时能及时发出警报；（2）乙系统失灵的条件下甲系统亦失灵？9．设B A ,为两随机变量，试求解下列问题：（1） 已知6/1)|(,3/1)()(===B A P B P A P 。
求：)|(B A P ； （2） 已知2/1)|(,3/1)|(,4/1)(===B A P A B P A P 。
课程大纲概率统计课程编号：02834720 授课对象：本科生学分：4 任课教师：涂云东课程类型：必修开课学期：2016年春先修课程：微积分，线性代数任课教师简历（500字左右）：涂云东，北京大学光华管理学院商务统计与计量经济系助理教授，于2012年获加州大学河滨分校经济学博士。
研究领域理论计量经济学应用计量经济学金融计量理论任课教师联系方式：办公电话：62760219,电子邮箱：yundong.tu@，办公室：光华新楼475助教姓名及联系方式：谢雨辰, xieyuchen@刘进, jin@郇钰, huanyu@辅导、答疑时间：课堂内安排及邮件预约一、项目培养目标Learning Goal 1: Graduates will possess a solid understanding of business and management and will be able to translate this knowledge into practice.1.1 Objective 1 Our students will have a good command of fundamental theories andknowledge.1.2 Objective 2 Our students will have a good command of analytical methods anddecision-making tools.1.3 Objective 3 Our students will be able to apply theories and methodologies in keybusiness functions.Learning Goal 2: Our students will be able to think critically.2.1 Objective 1 Our students will be able to identify and summarize problems2.2 Objective 2 Our students will be able to collect data and analyze problems in a criticalmanner2.3 Objective 3 Our students will be able to put forward effective solutions to businessproblemsLearning Goal 3:Our students will have a sense of social responsibility.3.1 Objective 1 Our students will be aware of the importance of ethics.3.2 Objective 2 Our students will be able to provide solutions that take account ofcontrasting ethical standpoints.Learning Goal 4: Our students will be effective communicators.4.1 Objective 1 Our students will be proficient in oral and written communication.4.2 Objective 2 Our students will possess good interpersonal skills.4.3 Objective 3 Our students will be able to adapt to diverse learning environments. Learning Goal 5: Our students will have global perspectives.5.1 Objective 1 Our students will be aware of social and cultural differences.5.2 Objective 2 Our students will be aware of the impact of globalization on businessoperations, opportunities, and challenges.Objective 3 Our students will be proficient in English.二、课程概述本课程将介绍在概率论与数理统计的基本知识，包括概率，条件概率，随机变量的期望和方差，各种概率分布，抽样分布，点估计，置信区间，假设检验，线性回归，方差分析等.三、课程目标学生应该理解和掌握概率论与数理统计的基本概念，学习常用的概率分布，并能进行基本的统计推论。
Homework8October26,20111.Suppose that X1,X2,...,X n form a random sample from a normal distribution forwhich both the mean and the variance are unknown.Find the M.L.E.of the0.95 quantile of the distribution,that is,of the pointθsuch that Pr(X<θ)=0.95.2.Let X1,X2,...,X n represent a random sample from each of the distributions havingthe following probability density functions:f(x;θ)=θxθ−1,0<x<1,0<θ<∞, zero elsewhere.Show that the m.l.e. θofθis consistent.3.Suppose that a random sample is to be taken from a normal distribution for which thevalue of the meanθis unknown and the standard deviation is2.(a)How large a random sample must be taken in order that E(|X n−θ|2)≤0.1forevery possible value ofθ?(b)How large a random sample must be taken in order that E(|X n−θ|)≤0.1forevery possible value ofθ?(c)How large a random sample must be taken in order that P r(|X n−θ|≤0.1)≥0.95for every possible value ofθ?4.(Textbook Section7.7-10,Page284)Suppose that a certain drug is to be administeredto two different types of animals A and B.It is known that the mean response of animals of type A is the same as the mean response of animals of type B,but the common valueθof this mean is unknown and must be estimated.It is also known that the variance of the response of animals of type A if four times as large as the variance of the response of animals of type B.Let X1,···,X m denote the responses ofa random sample of m animals of type A,and let Y1,···,Y n denote the responses ofan independent random sample of n animals of type B.Finally,consider the estimatorˆθ=αX+(1−α)Y n.m(a)For what values ofα,m and n isˆθan unbiased estimator ofθ?(b)Forfixed values of m and n,what value ofαyields an unbiased estimator withminimum variance?5.(Textbook Section7.4-2,Page270)Suppose that X1,···,X n form a random samplefrom a normal distribution for which the meanµand the standard deviationσare unknown,and letˆµandˆσdenote the M.L.E.’s ofµandσ.For the sample size n=17,find a value of k such that P r(ˆµ>µ+kˆσ)=0.95.6.(Textbook Section7.4-3,Page270)Suppose that thefive random variables X1,···,X5are i.i.d.,and each has a standard normal distribution.Determine a constant c suchthat the random variablec(X1+X2)(X23+X24+X25)1/2will have a t distribution.。
