homework1

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清华大学随机过程答案1

其中 n = 1, 2 . . . , k = 1, 2 . . .
3. 质点在直线上做随机运动，即在 t = 1, 2, 3, · · · 时质点可以在 x 轴上往右或往左做一个单位距离的随机游动。若往右移动一个单位距离的概率为 p，往左移动一个单位距离的概率为 q，即 P {ξ (i) = +1} = p，P {ξ (i) = −1} = q，p + q = 1，且各次游动是相互统 ∑n 计独立的。经过 n 次游走，质点所处的位置为 ηn = η (n) = ξi。
参考答案：
(1) V = a 时，一条样本轨道为典型的正弦曲线。 2
(2) ξ (0) = 0，fξ(0)(x) = δ(x)；ξ (π/2ω) = V ，其概率密度同 V 一样。
(π) ξ
4ω
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√ 2
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π 4ω
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=
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0
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xHale Waihona Puke <√a 2() 5π
ξ 4ω
=
V
−
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n
pmqn−m = pn − qn。
m=0
m
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解法二：因各次游走是相互统计独立的，则 E [η (n)] = E[ξi] = (p − q)n。
i=1
清华大学电子工程系版权所有
3
(2) 假设 n1 < n2,
Rηη (n1, n2) = E [η (n1) η (n2)] = E {η (n1) [η (n1) + η (n2) − η (n1)]} = E[η (n1)]2 + E [η (n1)] E [η (n2) − η (n1)] = {E [η (n1)]}2 + V ar [η (n1)] + (p − q)2n1 (n2 − n1) = (p − q)2n21 + n1V ar [ξi] + (p − q)2n1 (n2 − n1) = (p − q)2n1n2 + n1[1 − (p − q)2]

homework1

Homework for Solid’s Magnetism1, Pauli spin susceptibility. The spin susceptibility of a conduction electron gas at absolute zero temperature (T~0) may be discussed by another method. Letn +=n (1+η)/2; n -=n (1-η)/2be the concentration of spin-up and spin-down electrons.(1) show that in a external magetic field B 0, the total energy of the spin-up band in a free electron gas is),1(21-)(105/30ημηε++=+B n E B Where F n εε1030=, in terms of Fermi energy F ε in zero magnetic field (B 0=0). Also find a similar expression for E −.(2) Minimize -++=E E E total with respect to η and solve the equilibrium value of η in theapproximation 1<<η. Go on to show the magnetization is F BB n M εμ3/302=. 2，Diamagnetic susceptibility of atom hydrogen. The wave function of the hydrogen atom in itsground state (1s) is 0/2/130)(a r e a --=πψ, where cm 10529.0/8220-⨯==me a . The charge density is 2),,(ψρe z y x -=. According to the statistical interpretation of the wave function, showthat for this state 2023a r >=<, and calculate the molar diamagnetic susceptibility of atom hydrogen.3，Heat capacity of magnons. Use the approximation magnon dispersion relation 2ak =ωto the leading term in the heat capacity of a three-dimensional ferromagnet at low temperature. (k is the wavevector). (Integral: 772.1)333.1(4343)!23(112/512/501/2/32/3==≅==-∑∑⎰∑∞=-∞=-∞∞=-ππn n n x n x n n dx e x e dx x) 4，给定三个外观相同的物体：（1）永久磁体；（2）顺磁材料；（3）未磁化的铁磁材料。

homework_1

1.一线性连续系统在相同的初始条件下，当输入为f（t）时，全响应为y(t)=2e-t+cos2t，当输入2f（t）时，全响应y(t)=e-t+2cos(2t)。

求在相同的初始条件下，输入为4f（t）时的全响应。

2.已知系统的输入和输出关系为y(t)=|f（t）-f（t-1）|，试判断该系统：（1）是不是线性的？（2）是不是时不变的？（3）当输入f（t）如图1所示时，画出响应y(t)的波形。

图 13.一个LTI系统，当输入f（t）=ε(t)时，输出为y(t)=e-tε(t)+ε(-1-t)，求该系统对图2所示输入f（t）时的响应，并概略地画出其波形。

图21、给定系统微分方程，若系统起始状态为，分别就以下两种激励信号求系统的完全响应，并指出零输入响应和零状态响应分量。

2、给定系统微分方程，若系统激励信号，系统的起始状态为 y ( 0 - ) = 1 ， y ′( 0 - ) = 0，求系统的完全响应、零状态响应、零输入响应。

3、已知某系统对激励的完全响应为，对激励的完全响应为⑴ 求系统的零输入响应⑵ 若系统起始状态不变，求系统对激励的完全响应。

4、题图所示系统是由几个“子系统”组成，各子系统的冲激响应分别为： )()(1t u t h = （积分器） )1()(2-=t t h δ（单位延时） )()(3t t h δ-= （倒相器）试求总的系统的冲激响应)(t h 。

1、求图示频谱函数F （j ω）的傅里叶反变换，f （t ）=F -1[F （j ω）]，并画出f （t ）的波形图。

ω2、系统如题图（a ）所示，低通滤波器的传输函数如题图（b ）所示，已知()Sa(2)x t t π=，()()3n n s t t δ∞=-∞=-∑ω1．求信号的频谱)(t x =)(ωj X F )()],([ωj X t x 并画出～ω图形； 2．求输出信号y （t ），并粗略画出其波形。

3、题图所示系统，已知f 1（t ）= Sa （t ），(1+cos1000t)f 3(t )f 1(t )1．画出f 2（t ）的时域波形；2．求f 2（t ）的频谱函数F 2（j ω）= F [f 2（t ）]，并画出频谱图； 3．画出f 3（t ）的频谱图F 3（j ω）。

homework (1)-教育文档

Homework
要练说，先练胆。说话胆小是幼儿语言发展的障碍。不少幼儿当众说话时显得胆怯：有的结巴重复，面红耳赤；有的声音极低，自讲自听；有的低头不语，扯衣服，扭身子。总之，说话时外部表现不自然。我抓住练胆这个关键，面向全体，偏向差生。一是和幼儿建立和谐的语言交流关系。每当和幼儿讲话时，我总是笑脸相迎，声音亲切，动作亲昵，消除幼儿畏惧心理，让他能主动的、无拘无束地和我交谈。二是注重培养幼儿敢于当众说话的习惯。或在课堂教学中，改变过去老师讲学生听的传统的教学模式，取消了先举手后发言的约束，多采取自由讨论和谈话的形式，给每个幼儿较多的当众说话的机会，培养幼儿爱说话敢说话的兴趣，对一些说话有困难的幼儿，我总是认真地耐心地听，热情地帮助和鼓励他把话说完、说好，增强其说话的勇气和把话说好的信心。三是要提明确的说话要求，在说话训练中不断提高，我要求每个幼儿在说话时要仪态大方，口齿清楚，声音响亮，学会用眼神。对说得好的幼儿，即使是某一方面，我都抓住教育，提出表扬，并要其他幼儿模仿。长期坚持，不断训练，幼儿说话胆量也在不断提高。1. Oral work:
语文课本中的文章都是精选的比较优秀的文章,还有不少名家名篇。如果有选择循序渐进地让学生背诵一些优秀篇目、精彩段落,对提高学生的水平会大有裨益。现在,不少语文教师在分析课文时,把文章解体的支离破碎,总在文章的技巧方面下功夫。结果教师费劲,学生头疼。分析完之后,学生收效甚微,没过几天便忘的一干二净。造成这种事倍功半的尴尬局面的关键就是对文章读的不熟。常言道“书读百遍,其义自见”,如果有目的、有计划地引导学生反复阅读课文,或细读、默读、跳读,或听读、范读、轮读、分角色朗读,学生便可以在读中自然领悟文章的思想内容和写作技巧,可以在读中自然加强语感,增强语言的感受力。久而久之,这种思想内容、写作技巧和语感就会自然渗透到学生的语言意识之中,就会在写作中自觉不自觉地加以运用、创造和发展。2. Written work:

Homework1

Homework 1Please find out the mistakes in the translation(1), tell why they are wrong(2), and give a better translated version(3).大黄鱼产品简介东旭牌鲜咸大黄鱼获国家专利：ZL01311830.7，2001年获中国浙江国际农业博览会金奖，2002年获浙江农业博览会金奖及浙江农业博览会制定产品。

本产品采用东海鲜活大黄鱼，引进国外先进设备及科学配方，经特殊工艺精制脱脂而成，色鲜味佳，肉质细嫩，香咸可口，营养丰富，食而不腻。

含有人体所需多种维生素、蛋白质、钙、磷、铁、碘等，是宴客佳肴，馈赠亲朋好友及各单位发放福利的好礼品。

配料：鲜活大黄鱼、白砂糖、精制盐。

食用方法：清蒸、红烧、炖黄酒、微波炉烧烤味更佳（不需加盐、糖、味精）。

贮存方法：-10℃低温冷藏、防潮、防压。

生产日期：标示封口处保质期：6个月净重：660克±20克请消费者认准东旭牌商标，谨防假冒！BRIEF INTRODUCTIONDongxu Brand salted fresh large yellow croaker has got the national patent: ZL01311830.7. In 2001, it again won the gold prize of Zhejiang Agricultural Fair and the title of authorized product of the Fair. This product is processed by world-level advanced production facilities and special de-fatted technologies on basis of scientific formula, using live fresh g reater croaker from the Donghai Sea. It’s brilliant and fresh in color, good in taste, tender in flesh texture, proper in salty taste, and without being saturated in grease. Most of all, it’s loaded with rich nutrients essential to body such as vitamins, protein, and trace elements like Ca, P, Fe, and I. It’s ideal for use in feast, or as a gift.Ingredients: Live greater croaker, white granulated sugar, refined salt.Directions: Steam in clear soup, braise in soy sauce, stew with rice wine, better in taste if roast in microwave oven. (No necessary to add the salt, sugar, or MSG) Storage: Cold storage below-10℃; avoid moisture and pressure.Production Date: Show in the sealShelf Life: 6 monthsNet Weight: 660g±20gPlease identify clearly the trademark of Dongxu Brand; beware of imitations.1。

新9A第一单元Unit1Know yourself教案

Explain the important phrases and sentences in the dialogue.
Task4 Practice
1. Work in pairs and drill the dialogue.
2. Ask some Ss to act the dialogue out
3.To use adjectives to describe someone’s characteristics.
4: To improve Ss’ ability of reading comprehension and use adjectives to describe someone’s characteristics freely.
课题
Unit 1Comic strip and welcome to the unit
主备人
课型
新授
课时
1
总课时
6
教学设计
二次备课
教学目标
Students can talk about personalities.
Students can master some useful expressions.
(1) Is Wu Wei quiet?
(2) What did Su Ning do before he started to work for the sales department in a big company?
(3)What is Liu Hao’s job at present?
(4) What is Fang Yuan like?
1.Introduce your best friend with different adj .

Homework_1(Solution)

单选题（共计40题）1.若二进制数为010111.101，则该数的十进制表示为（B）。

A：23.5 B：23.625C：23.75 D：23.51252.11000110为二进制补码，该数的真值为（D）。

A： +198 B： -198C： +58 D： -583.01000110为二进制补码,该数的真值为（A）。

A： +70 B： -70C： +58 D： -584.字符A的A S C I I码为41H，字符a的A S C I I码为（C）。

A：41H B：42HC：61H D：62H5.字符9的A S C I I码为（C）。

A：09H B：9C：39H D：99H6.8位二进制数的原码表值范围为（C）。

A：0 ～ 255 B：-128 ～ +127C：-127 ～ +127 D：-128 ～ +1287.8位二进制数的反码表值范围为（C）。

A：0 ～ 255 B：-128 ～ +127C：-127～ +127 D：-128 ～ +1288.8位二进制数的补码表值范围为（B）。

A：0 ～ 255 B：-128 ～ +127C：-127 ～ +127 D：-128 ～ +1289.8位二进制数的无符号数表值范围为（A）。

A：0 ～ 255 B：-128 ～ +127C：-127 ～ +127 D：-128 ～ +12810.电子计算机遵循“存储程序”的概念，最早提出它的是（B）。

A：巴贝奇 B：冯．诺伊曼C：帕斯卡 D：贝尔11.决定计算机主要性能的是（A）。

C：存储容量 D：整机价格12.程序计数器P C的作用是（A）。

A：保存将要执行的下一条指令的地址 B：保存CPU要访问的内存单元地址C：保存运算器运算结果内容 D：保存正在执行的一条指令13.完整的计算机系统应包括（D）。

A：运算器、控制器、存储器 B：主机和应用程序C：主机和外部设备 D：硬件设备和软件系统14.下面关于C P U的叙述中，不正确的是（C）。

homework1

1、Design a class named Account that contains:■ A private int data field named id for the account (default 0).■ A private double data field named balance for the account (default 0).■ A private double data field named annualInterestRate that stores the cur-rent interest rate (default 0). Assume all accounts have the same interest rate.■ A private java.util.Date data field named dateCreated that stores the date when the account was created.■ A private String data field named customer that stores the name of the customer.■ A data field named transactions whose type is java.util.ArrayList that stores the transaction for the accounts. Each transaction is an instance of the Transaction class. The Transaction class is defined as shown in Figure 1.■ A no-arg constructor that creates a default account.■ A constructor that creates an account with the specified id and initial balance.■ A constructor that constructs an account with the specified name,id, and balance.■The accessor and mutator methods for id, balance, and annualInterestRate.■The accessor method for dateCreated.■ A method named getMonthlyInterestRate() that returns the monthlyinterest rate.■ A method named withdraw that withdraws a specified amount from the account and adds a transaction to the transactions array list.■ A method named deposit that deposits a specified amount to the account adds a transaction to the transactions array list.Tasks:A、Implement Account Class；B、Implement Transaction Class；C、Write a test program that creates an Account with annual interest rate 1.5%, balance 1000, id 1122, and name George. Deposit $30, $40, $50 to the account and withdraw $5, $4, $2 from the account. Print an account summary that shows account holder name, interest rate, balance, and all transactions.Notes：java.util.Date and java.util.ArrayList are implemented in the Java API.Figure 12、Implement xjtuse.ArrayList and the methods defined in Figure2. (Hint: Use an array to store the elements in ArrayList. If the size of the ArrayList exceeds the capacity of the current array, create a new array that doubles the size of the current array and copy the contents of the current to the new array.)Figure 2Tasks：A、Implement the xjtuse.ArrayList class;B、The xjtuse.ArrayList class takes the place of java.util.ArrayList calss in Account class.。

八年级上册英语第一单元教学设计

unit 1 where did you go on vacation?section a 1 (1a-2d)⼀、教学⽬标：1. 语⾔知识⽬标：1) 能掌握以下单词：anyone, anywhere, wonderful, quite a few, most, something, nothing, everyone, of course, myself, yourself能掌握以下句型：① —where did you go on vacation? —i went to the mountains.② —where did tina to on vacation? —she went to the beach.③ —did you go with anyone? —yes, i did./no, i didn’t.2) 能了解以下语法：—复合不定代词someone, anyone, something, anything等的⽤法。

—yourself, myself等反⾝代词的⽤法。

3）⼀般过去时态的特殊疑问句，⼀般疑问句及其肯定、否定回答。

2. 情感态度价值观⽬标：学会⽤⼀般过去时进⾏信息交流，培养学⽣的环保意识，热爱⼤⾃然。

⼆、教学重难点1. 教学重点：1) ⽤所学的功能语⾔交流假期去了什么旅⾏。

2) 掌握本课时出现的新词汇。

2. 教学难点：1) 复合不定代词someone, anyone, something, anything等的⽤法。

2) yourself, myself等反⾝代词的⽤法。

三、教学过程ⅰ. lead-in1. 看动画⽚来进⼊本课时的主题谈论上周末做了些什么事情，谈论过去发⽣的事情。

ⅱ. presentation1. show some pictures on the big screen. let ss read the expressions.2. focus attention on the picture. ask: what can you see? say: each picture showssomething a person did in the past. name each activity and ask students to repeat:stayed at home, went to mountains, went to new york city 6. went to the beach,visited my uncle, visited museums, went to summer camp3. now, please match each phrase with one of the pictures next to the name of theactivity，point to the sample answer.4. check the answers. answers: 1. f 2. b 3. g 4. e5. c6. a7. diii. listening1. point to the picture on the screen.say: look at the picture a. where did tina go on vacation? she went to mountains.ask: what did the person do in each picture?2. play the recording the first time.3. play the recording a second time.say: there are three conversations. the people talk about what did on vacation. listen to the recording and write numbers of the names in the right boxes of the picture.4. check the answers.iv．pair work1. point out the sample conversation. ask two ss to read the conversation to the class.2. now work with a partner. make your own conversation about the people in the picture.3. ss work in pairs. as they talk, move around the classroom and give any help they need.4. let some pairs act out their conversations.v. listening1. tell ss they will hear a conversation about three students’ conversations. listen for the first time and fill in the chart. then listen again and check yes, or no.2. let ss read the phrases in the chart of 2b.3. play the recording the first time. ss listen and fill in the chart.4. play the recording a second time for the ss to check “yes, i did.” or “no, i didn’t. ”5. check the answers with the ss.vi. pair work1. let two ss read the conversation between grace, kevin and julie.2. let ss work in pairs and try to role-play the conversation.3. ask some pairs to act out their conversations.vii. role-play1. first let ss read the conversation and match the people and places they went.2. let ss act out the conversations in pairs.3. some explanations in 2d.homework:⽤英语询问你的⼀位好朋友，她（他）假期去了哪⾥？看到了什么？并将此对话写在作业上。

人教版新起点一年级英语上册全册教案

Unit 1 Lesson 1This is the first lesson in this first unit. The main topic is the daily expression the primary student would use during the period of school, so improving the students’ abilities of the daily conversation is very important.【知识目标】Key vocabulary: book, ruler, pencil, eraser, pen, pencil, book, ruler, schoolbagKey structures: Show me your …I’m…【能力目标】To understand the language of class instruction, such as: stand up【情感目标】Cultivate students' interest in English activities【教学重点】Students can understand, speak, read and write vocabulary: Tomato, potato, candy, bag Students can understand and speak the following sentences: Show me your (book).Here it is.【教学难点】Learn self introduction and Good morning pronunciation.The consolidation of classroom discipline.Teaching recordings, pictures, word cards, teaching pictures and PPT courseware.Step 1. Warm UpLearn the song "Point at your eyes"The teacher with the singing and dancing learned English songs, stimulate students to participate in activities of desire.Step 2. The basic partTeachers show the objects of pen, pencil, book, ruler and schoolbag one by one, to guide the students to be bold in theory and to correct their pronunciation.Teacher: What is it?Student: It 's a (pencil). (no answer, the teacher takes a few times.)Teacher: What is it?Student: It 's a (pen)Teacher: What is it?Student: It 's a (book)Teacher: What is it?Student: It 's a (ruler)Teacher:What is it?Student: It 's a (schoolbag)Step 3. Presentation and Practice1.Teachers design the situation to help students understand :Show me your (Book).Here it is.Ask a student to hold a book, and the teacher holds out his hands and says Show me your (Book). Ask other students to practice the dialogue and pay attention to correct pronunciation.2.Guide the students to analogous:Show me your (pen, pencil, book, ruler, schoolbag).Here it is.Step 4. Game Playing1.A game: A student is asked to come to the stage with her eyes covered.The teacher is going to put pen, pencil, book, ruler and schoolbag on the floor.The teacher says, "Show me your (Book)", the student touches the object and says "Here it is."It's wrong to change to another student to play.Step 5. Home work和父母做一个游戏：父母拿出你的文具，你说出对应单词。

北航计算机研究生课程算法设计与分析HomeWork_1

一、已知下列递推式：C(n) = 1 若n =1= 2C （n/2） + n – 1 若n ≥ 2请由定理1 导出C(n)的非递归表达式并指出其渐进复杂性。

定理1：设a,c 为非负整数，b,d,x 为非负常数，并对于某个非负整数k, 令n=c k ,则以下递推式f(n) =d 若 n=1=af(n/c)+bn x 若 n>=2的解是f(n)= bnx log c n + dn x 若 a=c x f(n)= x x x ax xn c a bc n c a bc d c log 若 a ≠c x解：令F(n) = C(n) – 1则 F(n) = 0 n=1F(n) = 2C(n/2) + n – 2 n>=2= 2[F(n/2) + 1] + n – 2= 2F(n/2) + n利用定理1，其中：d=0,a=2,c=2,b=1,x=1,并且a=cx 所以 F(n) = nlog 2n所以 C(n) = F(n) + 1 = nlog 2n + 1C(n)的渐进复杂性是O(nlog 2n)二、由于Prim 算法和Kruskal 算法设计思路的不同，导致了其对不同问题实例的效率对比关系的不同。

请简要论述：1、如何将两种算法集成，以适应问题的不同实例输入；2、你如何评价这一集成的意义？答：1、Prim 算法基于顶点进行搜索，所以适合顶点少边多的情况。

Kruskal 从边集合中进行搜索，所以适合边少的情况。

根据输入的图中的顶点和边的情况，边少的选用kruskal 算法，顶点少的选用prim 算法2、没有一个算法是万能的，没有一个算法是对所有情况都适合的。

这一集成体现了针对具体问题选用最适合的方法，即具体问题具体分析的哲学思想。

三、分析以下生成排列算法的正确性和时间效率：HeapPermute (n)//实现生成排列的Heap 算法//输入：一个正正整数n和一个全局数组A[1..n]//输出：A中元素的全排列if n = 1write Aelsefor i ←1 to n doHeapPermute(n-1)if n is oddswap A[1]and A[n]else s wap A[i]and A[n]解：n=1时，输出a1n=2时，输出a1a2，a2a1n=3时，(1)第一次循环i=1时，HeapPermute(2)将a1a2做完全排列输出，记为[a1a2]a3，并将A变为a2a1a3，并交换1,3位，得a3a1a2(2)第二次循环i=2时，HeapPermute(2)输出[a3a1]a2，并将A变为a1a3a2，交换1,3位，得a2a3a1(3)第三次循环i=3时，HeapPermute(2)输出[a2a3]a1，并将A变为a3a2a1，交换1,3位，得a1a2a3，即全部输出完毕后数组A回到初始顺序。

Homework 1(A)

1
Macroeconomics Homework Assignment 1 Likewise, the optimal hiring of glue-guns K ∗ . 1 when L = 1 ........... (1 2 when L = 2 ........... (1 K∗ = 3 when L = 3 ........... (1 3 when L = 4 ........... (1
Due on Sep 25, Week 4
mark ) mark ) mark ) mark )
Note that there is an intersection of the optimal solutions. L∗ = 4 ................................... (2 marks) K ∗ = 3 ................................... (2 marks) We can then compute the maximum economic proﬁt. economic prof it = revenue − f ixed cost − labor cost − capital cost ...... (2 marks) π ∗ = $190 × 5 − $140 − 4 × $100 − 3 × $60 = $230 .......................................................................... (2 marks) 2. (20 marks) Suppose Penny further expand her business by hiring more workers (L) and glue-guns (K). Her production function is Cobb-Douglas: Y = AK α L1−α , where α = 0.3. (a) Assuming Penny’s business is competitive and proﬁt-maximizing, derive her MPL and MPK. 5 W = , what is the capital labor (b) If the ratio of wage rate and rental price is R 3 K ratio: ? L (c) A is also called the total-factor productivity (TFP), which measures the productivity of the available technology. Assuming with the help of her highly intelligent employees (three PhD and one Master in engineering), Penny is able to improve the TFP by 20%. How will that affect Penny’s demand for workers and glue-guns? Answers: (a) Penny’s marginal product of labor is MPL = dY = (1 − α)AK α L−α = 0.7AK 0.3 L−0.3 ...... (4 marks) dL

handwriting homework1dandan

Ⅱ.1.shocked: make someone feel very surprised and upset, and unable to believe what has happenedraging: very great and hard to controlslash: wave something stronglymocking: formal to laugh at someone or something and try to make them look stupid by saying unkind things about themamaze: it amazes somebody how/what2.shock=>astonish/surpriseThe original one has a better effect of expressing the astonishment .raging=>radical/ extremeThe original one has a stronger force.slash=>wave/shakeThe original one has a stronger force.mock=> deride\laugh atThe original one is formal.amaze=> astonish/astoundThe original one is a slang expression..Ⅳ.walk:jump,run,roll,track,pad,wendlook at:stare,watch,see,observe,viewcry:weep,sob（啜泣）,wailangry:indignant,furious,sulkytree:pine(松树)，maple(枫树)，willow（柳树）animal:cat,dog,pig,lion,donkey,bearflower:rose,carnation,tulip(郁金香),lily（百合）,sunflower（向日葵）wind:storm,hurricane,typhoonrain:shower,downpour,tempestⅤcontinue:go onendure:put up withinvestigate:look intoexpect:look forward todestroy:break downbuild:put upstart:set outpostpone:put offbegin to like:take toⅥ1.formal2.momentous decree、captivity、the manacles of segregation、the chains of discrimination、languish、dramatize、an appalling condition3. SimileThis momentous decree came as a great beacon light of hope to millions of negro...It came as a joyous daybreak ...MetaphorWho had been seared in the flames of withering injustice。

homework1-solution

2014 通信技术与系统作业1 参考答案授课教师: 梁菁2.某消息以二进制码方式传输，信息速率为2Mbps（1）若在接收机输出端平均每小时72个差错，求误比特率；（2）若已知信道的误比特率为5x10-9，求平均相隔多长时间就会出现1bit差错。

解(1)平均每秒钟723600=0.02个差错误比特率为p e=0.022×106=10−8(2) 信息速率R b=2(Mbit/s)P e=5×10−9平均每秒差错比特数N e=R b P e=2×106×5×10−9=0.01T e=1N e=100(s),即平均100秒产生1bit差错。

3-19. 已知有线电话信道的带宽为3.4KHz ：（1）试求信道输出信噪比为30dB 时的信道容量（2）若要在该信道中传输33.6kb/s 的数据，试求接收端要求的最小信噪比为多少。

解：（1） 10log (S N �)=30， S N �=1000信道容量C =B ×log 2(1+S N ⁄)=3.4×103×log 2(1+1000)=3.39×104(bit /s ) （2）传输速率R=33.6kb/s ≤C , 所以 R =C MIN =B ×log 2(1+S N ⁄MIN )求得接收端最小信噪比 S N ⁄MIN ≈942.8≈29.74dB6.设有一个照片要在电话线路中实现传真传输，要传输2.25×106个像素，每个像素有12个亮度等级。

假设所有的亮度等级都是等概率的，电话电路具有3kHz 带宽和30dB 的信噪比。

试求在该标准电话线路上传输一张传真图片需要的最小时间。

解：共有M=12个亮度等级，且等概率，故每个像素的平均信息量为H =log 2M =log 212=3.58(bit/像素)共有n =2.25×106个像素，一张图片的总信息量为I =Hn =3.58×2.25×106=8.06(Mbit )已知信噪比为30dB ，即10log �SN�=30，SN =1000信道容量C =Blog 2�1+SN �=3×103×log 2(1+1000)≈2.99×104(bit /s )最大信息速率R max =C =2.99×104(bit /s ) 所以最小传输时间T min =IR max =8.06×1062.99×104=2.69×102(s )=4.5(min )7.Matlab 仿真(1) 用Matlab 产生一个均值为10，方差为4的高斯噪声信号序列, 序列长度500, 分别画出时域波形图和概率分布图，并求该序列的均值和方差, 自相关函数和功率谱密度。

小升初E6homework1-10

Exercise1Name:__________Date:_________score：_______I.Multiple Choice.1.____________news.A.What goodB.How goodC.What a goodD.How a good2.Dad,I have passed the exam.________A.Never mindB.Good luckC.Well doneD.All right3.About________of the workers in the factory were born in the________.A.two-third,1970B.two-thirds,1970sC.two-thirds,1970D.two-third,1970s4.How far is your cousin’s home from here?It’s about two_______drive.A.hour’sB.hoursC.hours’D.hour5.What is your favorite sport?Swimming,I think.It’s__________of all.A.easierB.more difficultC.the most interestingD.the most boringII.Choose the best answer.A:How are you?B:______6_________A:It’s a great party,_____7________B:Yes,it is.Do you like the music?A:____8________I play this kind of music with my band.B:You’re in the band?A:Yeah,_____9__________B:Really?Well,I work on the Internet all my free time.A:______10_______B:You are right,it is cool.A.What do you mean?B.Isn’t it?C.That sounds good.D.Oh,no.What a pity!E.we play in our free timeF.I love it.G.Fine,thanks.6________7_________8__________9________10________完形填空。

Homework 常见的技巧1

Homework (due in two weeks):1.One after another, speakers called for the downfall ofimperialism, abolition of exploitation of man by man, liberation of the oppressed of the word. 发言人相继呼吁要打倒帝国主义,消灭人剥削人的制度,解放全世界被压迫的人民。

2. A view of Mt. Fuji can be obtained from here.在这儿可以看到富士山。

3.She had high praise for Dr.Higpan, although she complainedabout his strictness. 她高度赞扬了西格潘医生,但抱怨他过于严格。

4.Up the street they went, past stores, across a broad square,and then entered a huge building.他们沿着大街走去，经过商店，穿过一个宽阔的广场，接着进入一座巨大的建筑。

5.I would usually first overfly Cyprus, with cameras on to see ifa fleet was being assembled there.我通常都会先飞越塞浦路斯，手上拿着照相机，看看是否有舰队聚集在那里。

6.The landing was designed to cut the peninsula in two.登陆的目的是把潘尼苏拉半岛一分为二。

7. A well-dressed man, who looked and talked like an American,got into the car.一个衣装得体，看起来和说起话来都像美国人的男子上了车。

中宏作业Homework_1-答案及部分解析

Intermediate MacroeconomicsSpring 2012 Problem Set 1评分标准：1.总分100分，错误题目扣分从100分起扣，最低为70分，不再继续往下扣分。

2. 选择题每题3分，其中第7,9题不计分，选错为0分，若选错但在解释答案是有合理成分的，可以得1到2分。

3. 2,3,5,6,7题每题10分。

4. 第4题不计分。

1.Multiple choice1) Primarily, macroeconomists use microeconomic principles to study A) business cycles and trends in the stock market. B) long-run economic growth and antitrust policies.C) trends in the stock market and long-term economic growth. D) long-run economic growth and business cycles. Answer: D2)The relationship between the level of growth of an economic variable, g t , and its level, y t , is best approximated as A) g t =y t y t 1.B) g t = log y t - log y t -1. C) y t = log g t - log g t -1. D) log g t = y t - y t -1.Answer: B3) The business cycle component of the log of real per-capita GNP is equal to A) log of actual real GNP - log of trend GNP. B) log of trend GNP ÷ log of actual real GNP. C) log of trend GNP - log of actual real GNP. D) log of actual real GNP ÷ log of trend GNP. Answer: A4) For the study of economic growth, it is most helpful to examine movements in ________; for the study of business cycles, it is most helpful to examine movements in ________.A) trend GNP; trend GNPB) trend GNP; deviations from trend in GNPC) deviations from trend in GNP; trend GNPD) deviations from trend in GNP; deviations from trend in GNPAnswer: B5) Suppose that GDP is equal to 1000, national saving is equal to 200, the current account deficit is equal to 100, and the government budget deficit is equal to 50. Investment must equalA) 150.B) 200.C) 250.D) 300.Answer: D6) When we try to measure real GDP and the price level, if we underestimate the growth in real GDP, we willA) always underestimate the rate of inflation.B) sometimes underestimate the rate of inflation.C) always overestimate the rate of inflation.D) sometimes overestimate the rate of inflation.Answer: CFor the following questions, suppose an economy produces only pens and pencils, and that the quantity and price data is given by this table:7)What is the real GDP in year 2 using base year 1?A) $418B) $300.C) $360.D) $338.Answer: D注：本题答案有错，应该是348.8) What is the real GDP in year 2 using base year 2?A) $418.B) $300.C) $360.D) $338.Answer: A9) What is approximately the growth rate of real GDP using base year 1?A) 13%B) 20%C) 33%D) 39%注：本题答案有错，应该是16%。

homework1-2010

a a+b a a+b b a+b 1 a+b
b b . a a
,
a b =1− a+b a+b
1−
b a+b
.
Now the theorem in the n = 2 case can be expressed as Pk −→ 1−
a a+b a a+b b a+b b a+b
1−
for k → ∞
This completes the proof of (2) and thereby the proof of the theorem in the case of 2×2 probablility matrices. Note that to prove the theorem in this case we did not actually need to have a, b ∈ (0, 1). It is enough to have a, b ∈ [0, 1] and a, b not both equal to 0 or 1. This is enough to ensure x = 1 − (a + b) satisﬁes |x| < 1, which is what we need for the above proof to work.
(∗)
We will prove the theorem (∗) in 2 steps: (1) Show that, for all n, Pk = where sk = 1 + x + x2 + · · · + xk (2) Show that sk → 1 a+b , x = 1 − (a + b). 1 − ask bsk ask 1 − bsk