Homework1_solution
清华大学随机过程答案1
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
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xHale Waihona Puke <√a 2() 5π
ξ 4ω
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pmqn−m = pn − qn。
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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]
HowtoDoYourHomework
WINNING AT MATHHOW TO DO YOUR HOMEWORKDoing your homework can be frustrating or rewarding. Most students jump right into their homework, become frustrated and stop studying. These students usually go directly to the math problems and start working them without any preparation. When they get stuck on one problem, they flip to the back of the text for the answer. Then, they either try to work the problem backward, to understand the problem steps, or they just copy down the answer.Other students go to the solution guide and just copy the steps. After getting stuck several times, these students will inevitably quit doing their homework assignment. Their homework becomes a frustrating experience, and they may even quit doing their work altogether.To improve your homework success and learning, refer to the following 10 steps:10 Steps to Doing Your HomeworkStep 1 - Review the textbook material that relates to the homework. A proper review will increase the chances of successfully completing your homework. If you get stuck on a problem, you will have a better chance of remembering the location of similar problems. If you do not review prior to doing your homework, you could get stuck and not know where to find help in the textbook.Remember: To be successful in learning the material and in completing homework assignments, you must first review your textbook.Step 2 - Review your lecture notes that relate to the homework. If you could not understand the explanation of the textbook on how to complete the homework assignment, then review your notes.Remember: Reviewing your notes will give you a better idea about how to complete your homework assignment.Step 3 - Do your homework as neatly as possible. Doing your homework neatly has several benefits. When approaching your instructor about problems with your homework, he or she will be able to understand your previous attempts to solve the problem. The instructor will easily locate the mistakes and show you how to correct the steps without having to decipher your handwriting. Another benefit is that, when you review for midterm or final exams, you can quickly relearn the homework material without having to decipher your own writing. Remember: Neatly prepared homework can help you now and in the future.Step 4 - When doing your homework, write down every step of the problem. Even if you can do the step in your head, write it down anyway. This will increase the amount of homework time, but you are overlearning how to solve problems, which improves your memory. Doing everystep is an easy way to memorize and understand the material. Another advantage is that when you rework the problems you did wrong, it is easy to review each step to find the mistake.Remember: In the long run, doing every step of the homework will save you time and frustration.Step 5 - Understand the reasons for each problem step and check your answers. Do not get into the bad habit of memorizing how to do problems without knowing the reasons for each step. Many students are smart enough to memorize procedures required to complete a set of homework problems. However, when similar homework problems are presented on a test, the student cannot solve the problems. To avoid this dilemma, keep reminding yourself about the rules, laws, or properties used to solve problems.Example: Problem 2(a+5) = 0. What property allows you to change the equation to 2a + 10 = 0? Answer: The distributive property.Once you know the correct reason for going from one step to another in solving a math problem, you can answer any problem requiring that property. Students who simply memorize how to do problems instead of understanding the reasons for correctly working steps will eventually fail their math course.How to Check Your AnswersChecking your homework answers should be part of your homework duties. Checking your answers can improve your learning and help you prepare for tests.Check the answers of the problems for which you do not have the solutions. This may be the even-numbered or odd-numbered problems or the problems not answered in the solutions manual.First, check your answer by estimating the correct answer.Example: If you are multiplying 2.234 by 5.102 the answer should be a little over 10. Remember that 2 times 5 is 10.You can also check your answers by substituting the answer back into the equation or doing the opposite function required to the question. The more answers you check, the faster you will become. This is very important because increasing your answer checking speed can help you catch more careless errors on future tests.Step 6 - If you do not understand how to do a problem refer to the following points:•Point 1 - Review the textbook material that relates to the problem.•Point 2 - Review the lecture notes that relate to the problem.•Point 3 - Review any similar problems, diagrams, examples or rules that explain the misunderstood material.•Point 4 - Refer to another math textbook, solutions guide, math computer program software or video tape to obtain a better understanding of the material.•Point 5 - Call your study buddy.•Point 6 - Skip the problem and contact your tutor or math instructor as soon as possible for help.Step 7 - Always finish your homework by successfully completing problems. Even if you get stuck, go back and successfully complete previous problems before quitting. You want to end your homework assignment with feelings of success.Step 8 - After finishing your homework assignment, recall to yourself or write down the most important learned concepts. Recalling this information will increase your ability to learn these new concepts. Additional information about Step 8 will be discussed later in this chapter.Step 9 - Make up note cards containing hard-to-remember problems or concepts. Note cards are an excellent way to review material for a test. More information on the use of note cards as learning tools is presented later in this chapter.Step 10 - Getting behind in math homework is academic suicide. Math is a sequential learning process. If you get behind, it is difficult to catch up because each topic builds on the next. It would be like going to Spanish class without learning the last set of vocabulary words. The teacher would be talking to you using the new vocabulary, but you would not understand what was being said.Do Not Fall BehindTo keep up with your homework, it is necessary to complete the homework every school day and even on weekends. Doing your homework one-half hour each day for two days in a row is better than one hour every other day.If you have to get behind in one of your courses, make sure it is not math. Fall behind in a course that does not have a sequential learning process, such as psychology or history. After using the 10 Steps to Doing Your Homework, you may be able to combine two steps into one. Find your best combination of homework steps and use them.Remember: Getting behind in math homework is the fastest way to fail the course.。
Homework5
SOLUTIONS FOR HOMEWORK FIVE1.Let H and K be subgroups of a group G,and K¡G.Prove that HK/K∼= H/H∩K.Proof.Note that HK≤G and K¡HK since K¡G.Setf:H→HK/Kh→hKThen f is a surjective group homomorphism since HK/K={hK|h∈H},and kerf={h∈H|hK=K}=H∩K.So we have HK/K∼=H/H∩K.P 2.Let K⊂H⊂G be subgroups of afinite group G.Prove the formula[G:K]= [G:H][H:K].Solution.By Lagrange’s Theorem,we have|G|=[G:K]|K||G|=[G:H]|H||H|=[H:K]|K|Thus[G:K]|K|=|G|=[G:H]|H|=[G:H][H:K]|K|,i.e.,[G:K]=[G:H][H:K].P3.Let H and K be subgroups of a group G,and let g∈G.The setHgK={x∈G|x=hgk for some h∈H and k∈K}is called a double coset.(a)Prove that the double cosets partition G.(b)Do all double cosets have the same order?Proof.(a)Since G=g∈GHgK,it suffices to show any two double cosets are either equal or disjoint.Suppose that Hg1K∩Hg2K=∅,g1,g2∈G,i.e.,there exist some h1,h2∈H and k1,k2∈K such that h1g1k1=h2g2k2.Then g1=h−1 1h2g2k2k−11∈Hg2K,and so Hg1K⊂Hg2K.Conversely,Hg2K⊂Hg1K andthen Hg1K=Hg2K.(b)All double cosets need not have the same order.Consider G=S3,and let H=K={(1),(12)}.Then we have|H(1)K|=2,but|H(13)K|=4.P 4.Let G be afinite group,N¡G,and|N|and|G/N|be coprime.If a∈G and the order of a divides|G/N|,then a∈N.1Proof.Set m=|G/N|and n=o(a).Then(m,n)=1since(m,|N|)=1and n||N|,and so there exist two integers s,t such that ms+nt=1.Since(aN)m=Ni.e.,a m∈N,so a=a ms+nt=(a m)s(a n)t=(a m)s∈N.P5.Let G be a group,c∈G,and the order of c is rs,where(r,s)=1.Prove that there are elements a and b of G such that c=ab and the order of a and b are r and s respectively,and ab=ba.Proof.Since(r,s)=1,there exist two integers m,n such that mr+ns=1.Set a=c ns and b=c mr.Then o(a)=r,o(b)=s and ab=c=ba.P2。
人教版八年级英语Unit 9-Unit 10【复习课件】-2023年中考英语一轮大单元复习(人教版)
upset .
10.除非我们跟他人交谈，否则我们肯定会感觉更糟。
Unless we talk to someone，we'll certainly feel
11.如果我告诉我的父母，他们会生气的。
If I tell my parents，they'll be angry .
worse .
上一页 返回导航 下一页
for
an exam .
2.很抱歉，我没有空。这个周末我有很多家庭作业。
I'm sorry.I'm not available ．I have too
much homework
this weekend.
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3.我记得去年秋天他来看你的时候，我们一起去骑过自行车。
I remember we went bike riding together last fall when he
Friday，December 20th.
8.如果他们今天举t today， half
the
class won't come.
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9.如果我去参加聚会，他们会难过的。
If I go to the party，they will be
visited you.
4.周一晚上你能和我们一起逛逛吗？
Can you hang out with us on Monday night？
5.这个月末，我们全家打算去武汉旅行，看望我的婶婶和叔叔。
My family is taking
a
trip to Wuhan at the end of this
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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）。
Homework5_2013_solution1
3.21 Consider the M/M/1/m system which is the same as M/M/1 except that there can be no more than m customers in the system and customers arriving when the system is full are lost. Show that the steady-state occupancy probabilities are given by()m n p m n n ≤≤--=+0,111ρρρ证明：方法1， 直接使用系统状态变化的马氏链去计算方法2，可以使用截断马氏链的结果去做3.55 Consider the feedback model of a CPU and I/O device of Example 3.19 with the difference that the CPU consists of m identical parallel processors. The service time of a job at each parallel processor is exponentially distributed with mean 1/μ1. Derive the stationary distribution of the system.Solution:3.57 Consider the network in Fig 3.39. There are four sessions: ACE, ADE, BCEF, and BDEF sending Poisson traffic at rates 100, 200, 500, and 600 packets/min, respectively. Packet lengths are exponentially distributed with mean 1000 bits. All transmission lines have capacity 50 kbits/sec, and there is a propagation delay of 2 msec on each line. Using the Kleinrock independence approximation, find the average number of packets in the system, the average delay per packet (regardless of session), and the average delay per packet of each session.Figure 3.39Solution ：参考P211， section 3.6.1详细过程略。
那天我解决了一个麻烦英语作文60词
那天我解决了一个麻烦英语作文60词全文共10篇示例，供读者参考篇1One day, I solved a big problem! It was a really tricky one, but I managed to figure it out in the end.It all started when I was doing my homework. I had to solve a math problem that was really hard. I tried and tried, but I just couldn't get the right answer. I felt so frustrated and upset. I even asked my mom for help, but she didn't know how to solve it either.I didn't give up though. I kept trying different ways to solve the problem. I asked my friends for help, and we worked on it together. We tried drawing diagrams, using different methods, and finally, after a lot of hard work, we got the right answer!I was so happy and proud of myself. I couldn't believe that I had actually solved the problem that seemed impossible at first. It taught me that with hard work and perseverance, I can overcome any challenge that comes my way.So, that day, I learned an important lesson. No matter how difficult a problem may seem, if I keep trying and never give up, I can find the solution. I felt like a little detective who cracked the case. It was a great feeling!I was so excited to tell my teacher about it the next day. She was really impressed and gave me a big high five. I felt like a hero!From that day on, whenever I face a difficult problem, I always remember that day when I solved the tricky math problem. It gives me the confidence and determination to keep pushing forward and never give up.And that's the story of how I solved a big problem and learned an important lesson. It was a day I'll never forget!篇2Title: The Day I Solved a ProblemOne day, I had a big problem to solve. It was my math homework! I couldn't understand how to do long division and I was feeling really frustrated. But I didn't give up. I decided to ask my friend Tim for help.Tim is really good at math and he explained to me how to do long division step by step. He was so patient and kind, and soon I began to understand it better. I practiced a lot with Tim's help and little by little, I got better at it.After a few days of hard work, I finally managed to solve all the long division problems on my own. I was so happy and proud of myself! I couldn't believe how far I had come from feeling confused and stuck.I learned that it's okay to ask for help when you need it and that with perseverance and practice, you can overcome any challenge. I also learned the importance of not giving up and believing in yourself.Now, whenever I face a problem, I remember the day I solved my math homework and it gives me the confidence to keep trying. I know that with determination and a positive attitude, I can overcome any obstacle that comes my way.篇3One day, I had a big problem to solve. It was an English assignment that I just couldn't figure out. I had to write a story using all the vocabulary words we had learned that week, but I was stuck.I tried asking my mom for help, but she was busy cooking dinner. Then I asked my big brother, but he just laughed and said I should do it myself. I felt so frustrated and worried that I wouldn't be able to finish it on time.After dinner, I decided to take a break and watch my favorite cartoon. Suddenly, a light bulb went off in my head. I could use the characters and plot from the cartoon to create my story. It was like a light bulb going off in my head.I grabbed my notebook and started writing down ideas. I used all the vocabulary words in creative ways and before I knew it, I had a story that I was proud of. I showed it to my mom and brother, and they were both impressed.I learned that sometimes, the best way to solve a problem is to take a break and think outside the box. I was so happy that I was able to solve my problem and complete my assignment. It was a great feeling of accomplishment!篇4That day, I had a big problem to solve. It was a math problem and I just couldn't figure it out. I asked my mom for help, but she was busy cooking dinner. So, I decided to try to solve it on my own.I started by reading the problem carefully. It was about finding the area of a triangle, and I had to use a formula to solve it. I remembered my teacher explaining the formula in class, so I tried to remember what she had said.After a few tries, I finally got the answer! I was so happy and proud of myself for figuring it out. I couldn't wait to tell my mom and show her that I could solve the problem on my own.When my mom saw the answer, she was so impressed. She gave me a big hug and told me how proud she was of me. I felt really good about myself and I realized that I can do anything if I put my mind to it.From that day on, I always try to solve problems on my own before asking for help. I know that I am capable of figuring things out and I can't wait to tackle more challenges in the future.篇5That day, I had a big problem to solve. It all started when I realized my homework was missing! I searched everywhere in my backpack, in my room, and even asked my mom if she saw it. But it was nowhere to be found.I started to panic because I had worked really hard on that homework and I didn't want to get a bad grade. I knew I had to find a way to solve this problem. So, I took a deep breath and thought about what I could do.First, I retraced my steps to see if I could remember where I had last seen my homework. I remembered that I had it with me when I went to my friend's house to study. So, I called my friend and asked if I had left it there. And guess what? It was at her house!I was so relieved and happy that I found my homework. I quickly went to her house to pick it up and completed it before the deadline. I learned a valuable lesson that day – always double check where you last had something before panicking.I was proud of myself for solving this problem on my own. It taught me that I can overcome challenges if I stay calm and think logically. It was a tough situation, but I managed to find a solution. I felt like a superhero saving the day!And that's how I solved a big problem that day. It was a lesson that I will never forget.篇6That day I solved a big problemOne day, when I was playing with my friends in the playground, I realized that I forgot to bring my lunch box to school. I felt so worried because I didn't know what to do. I couldn't ask my friends for food because they already had their own lunch. I was really hungry and didn't know how to solve this problem.I thought about it for a while and then I remembered that my teacher always kept some extra snacks in her drawer for emergencies. So I went to my teacher and explained the situation to her. She was very understanding and gave me some crackers and a juice box to eat. I was so relieved and thankful to her for helping me out.After eating the snacks, I felt much better and was able to focus on my lessons for the rest of the day. I also made sure to remind myself to always double check my backpack before leaving the house to avoid forgetting things in the future.I learned that it's important to stay calm and think of solutions when faced with a problem. I was proud of myself for solving the issue and grateful to my teacher for being so kind and helpful.篇7One day, I had a big problem to solve. It all started when I forgot to bring my homework to school. I was so worried because I knew my teacher would be very angry with me.During the first break, I told my friend Lily about my problem. She suggested that we could try to finish the homework during lunchtime. I was a bit hesitant at first because I wasn't sure if we could do it in such a short time. But Lily was very confident and told me that we could do it together.During lunchtime, we found a quiet spot in the playground and started working on our homework. Lily was really good at English, so she helped me with the difficult parts. We worked quickly and efficiently, and before we knew it, we had finished the homework!I was so relieved and grateful to Lily for helping me out. When we handed in our homework to the teacher, she was surprised and impressed by how fast we had completed it. She even praised us in front of the whole class!From that day on, I learned that it's important to not give up when faced with a problem. By working together with a friend and staying positive, we can overcome any difficulties that comeour way. I was really proud of myself for solving the problem, and I knew that I could count on my friends for help whenever I needed it.篇8One day, I solved a tricky problem and I want to tell you all about it! It was a sunny morning when my teacher gave us a really hard English homework. We had to write a short story using past tense verbs. I was really worried because I wasn't sure if I could do it.When I got home, I sat down at my desk and started thinking about what to write. I knew I had to come up with a good story to impress my teacher. After a while, I finally got an idea for a story about a superhero who saved a cat from a tree. I quickly wrote down my story, making sure to use lots of past tense verbs.But then, when I read it back, I realized I had made a mistake.I had used present tense verbs instead of past tense verbs in some parts of my story. I was really frustrated and didn't know what to do. But then, I remembered something my teacher always says - "Never give up, keep trying!"So I took a deep breath, erased the wrong verbs, and replaced them with the correct ones. It took me a while, but I finally finished my story with all past tense verbs. I felt so relieved and proud of myself for solving the problem.The next day, I handed in my homework to my teacher. She read my story and gave me a big smile. She said she was really impressed with my effort and that my English was getting better every day. I was so happy to hear that and I knew that all my hard work had paid off.From that day on, I never gave up when faced with a tricky problem. I always try my best and remember that with a little perseverance, anything is possible. I learned that even if something seems difficult at first, I can overcome it with hard work and determination. And that's the story of how I solved a tricky English homework assignment!篇9That Day I Solved a Big ProblemOne day, I had a big problem. It was a really tough one. I had to solve it all by myself. I was so worried and scared. But I didn't give up. I knew I could do it!The problem was with my math homework. I had to solve some really hard equations. I didn't understand them at first. But then I remembered what my teacher taught me. I took a deep breath and started to work on them.I used my fingers to count and my brain to think. I wrote down all the numbers and symbols. I checked my work over and over again. Finally, I got the answer! I was so excited and proud of myself. I did it!I showed my math homework to my mom. She was so happy and proud of me too. She gave me a big hug and a high five. I felt like a superhero who just saved the day!From that day on, I knew I could solve any problem that came my way. I just had to believe in myself and never give up. I learned that with hard work and determination, anything is possible.I can't wait for the next challenge to come my way. I know I'll be ready for it! Bring it on!篇10One day, I had a big problem to solve. It all started when I couldn't find my favorite toy, Mr. Fluffytail. I looked everywherein my room, but he was nowhere to be found. I was so worried and upset because Mr. Fluffytail is my best friend and I couldn't imagine not having him with me.I decided to ask my mom for help. She suggested that we should retrace my steps and think about where I had been that day. So, we went to the park where I had played in the morning, but still no sign of Mr. Fluffytail. Then we went to the supermarket where we had bought groceries, but he wasn't there either.Finally, we went back home and started searching the house again. After a while, I remembered that I had left Mr. Fluffytail in the living room yesterday. So, we checked there and voila! There he was, sitting on the sofa looking all fluffy and cute.I was so relieved and happy to have found him. I learned that sometimes when you have a problem, you just need to stay calm, think logically, and ask for help. I was grateful to my mom for helping me solve the problem and now Mr. Fluffytail will never leave my side again.。
理工英语1作业1答案
理工英语(yīnɡ yǔ)1作业1答案理工英语1作业(zuòyè)1答案理工(lǐɡōnɡ)英语1作业1一、ion:underline;'>交际(jiāojì)用语1.-I’m so excited to meet you. May I introduce myself to you?C. You are welcome.2.-What’s your present job?C. I’m a film-maker.3.-Goodbye, everyone.-Bye, Sally! ______ Don’t forget to write.A. Stay in touch.4.-We’d be pleased if you could join us for dinner.B. Yes, I’d love to.5.-Welcome back, Mr. Smith! How about your business trip in Japan?B. Oh, fantastic! Mr. Mark is so satisfied with our project.二、词汇(cíhuì)与结构6.-Each apartment only ____ 15 to 30 square meters for one unit.C. takes7.-Can I help you, sir?-I’d like to have 100 ____. I want my students to draw pictures.A. piece of paper8.-You know, this bridge ____ Hong Kong, Zhuhai and Macau.C. contacts9.-One day they crossed the ____ bridge behind the palace.A. old Chinese stone10.-This box is ____ that one.B. as heavy as11.-I hope you’ll ____ working with us in the future.C. achieve12.-Let’s meet at 7:30 outside the gate of ____.A. the People’s Park13.-I really like that car you ____ and I am thinking of buying it.A. recommended14.-Sonia, do you think you are different from Linda?-Yes, I’m ____ at drawing than her.A. better15.-I’d love to ____ with you my new kitchenware.A. share16.-People who do not have wood must spend large amounts of money ____ cooking fuel.B. on17.-Nick ____ a job in a bank, but to our surprise, he didn’t take it.A. offered18.-We ____ two railway tickets online this Monday.B. booked19.-This article deals with the natural phenomenon which ____ mostinteresting to everyone.B. is20.-It was ____ who wrote those words on the blackboard.B. him三、阅读(yuèdú)理解21.-The best title this passage is ____.C. Planning a House22.-The first thing for a person to build a house is ____.C. to work out a plan23.-The phrase “draw a plan” in this passage means ____.C. working out a plan24.-When the builder starts to build a house, his estimate will have to be corrected and revised because ____.C. the prices of building materials and the expenses(费用(fèi yong)) of labormay be different from the original prices and expenses.25.-What is the relationship(关系(guān xì)) between the estimate and the plan?C. The estimate and the plan depend on each other.( T )26. The world’s longest high-speed railway route is from Beijing by Guangzhou.( F )27. It takes only 10 hours from Guangzhou to Beijing by train.( T )28. The opening of the Beijing to Zhengzhou section has linked with the total route.( T )29. The Beijing-Guangzhou line connects one third of China’s population and more than40 percent of its economic power.( F )30. These 350 kilometer per hour high-speed railway trains have made the country’s vast territory “considerably smaller”, andchanged the country economically.四、翻译(fānyì)31. That’s why tiny little apartments with bedroom, a kitchen and abathroom come into being.C. 这就是只有一卧一厨一卫的微型公寓(gōngyù)形成的原因。
英语九年级Unit1Howcanwebecomegoodlear
Please try to talk with your friends in English as much as possible.
1c Listen and complete the learning challenges he talks about.
➢ Challenges & Solutions
Lead in
How do you study English?
I study English … • by listening to tapes. • by studying with a group. • by watching English programs on TV. • by enjoying English songs. • by taking part in (烟台中考) In recent years the economy of our country _____ rapidly.
A. is increased B. has increased
C. increased
D. has been increased
答案： B
【解析】由时间状语 in recent years 得知，用现在完 成时；句意是：“近几年，我国的经济迅速增长 ” 。此句中 increase 不能用于被动语态，故选 B 。
• by asking the teacher for help. • by reading English magazines and newspapers. • by surfing the Internet. • by making word cards. • by reading the textbook.
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。
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Homework1：（(Important deadline: submit your homework on next Saturday, Oct. 17, 2009）
Questions ( from Data Networks) list:
3.6 A person enters a bank and finds all of the four clerks busy serving customers. There are no other customers in the bank, so the person will start service as soon as one of the customers in service leaves. Customers have independent, identical, exponential distribution of service time. (a) What is the probability that the person will be the last to leave the bank assuming that no other customers arrive?
(b) If the average service time is 1 minute, what is the average time the person will spend in the bank?
(c) Will the answer in part (a) change if there are some additional customers waiting in a common queue and customers begin service in the order of their arrival?
Solution：(a) 当该人开始接受服务时，其他3人的服务尚未结束，所有人剩下的服务时间仍为相同的指数分布。
因此这个人最后离开的概率是1/4。
(b) 该人从进入银行到接受服务的时间等于min(X1,X2,X3,X4)，其中X1,X2,X3,X4为正在接受服务的4个客户的剩余服务时间。
则
P[min(X1,X2,X3,X4)>x]=exp(-4μx)，为指数分布，均值=1/(4u)=0.25分钟。
所以该人在银行平均停留时间为1.25分钟。
(c) 不变。
不管队列中有多少客户，当该人开始接受服务时，情况仍与(a)相同，所有人剩余服务时间仍为相同的指数分布。
3.8 Consider a packet stream whereby packets arrive according to a Poisson process with rate 10 packets/sec. If the interarrival time between any two packets is less than the transmission time of the first to arrive, the two packets are said to collide. (This notion will be made more meaningful in Chapter 4 when discuss multi-access schemes.) Find the probabilities that a packet does not collide with either its predecessor or it successor and that a packet does not collide with another packet, assuming:
(a) All packets have a transmission time of 20 msec. (Answer: both probabilities are equal to 0.67)
(b) Packets have independent, exponentially distributed transmission time with mean 20 msec. (This part requires the M/M/∞ results.) (Answer: The probability of no collision with predecessor or successor is 0.694. The probability of no collision is 0.682)
Solution：(a) 设packet与前一个之间的到达间隔为τ1，与后一个之间的到达间隔为τ2，则与前后都不碰撞的概率
P=P[τ1>0.02]P[τ2>0.02]=e -2λ*0.02= e -2*10*0.02
和任何一个packet都不碰撞的概率与此相同。
(b)(1).P[no collision with predecessor or successor]=
P[τ2>s1] P[τ3>s2],其中, s1和s2分别为predecesor的传输时间和successor的传输时间.因为这些都是指数分布的独立的随机变量,所以,应用以下公式（习题3.12,或讲稿）,得到：
P[no collision with predecessor or successor]＝((μ/（λ+μ))^2 ,将λ＝10和μ＝1/0.02,代入上式得0.694. (2).P[no collision]＝P[zero customers in M/M/∞and no arrival during his service]＝e-λ/μP[τ>s],τ为下一到达间隔,s为服务时间.经计算可得该概率值为0.682.
上式的前一项即为队长是0的概率。
Questions from Kleinrock’s book (Queueing theory V ol.1):
2.1 Consider K independent sources of customers where the interarrival time between customers
(i. e. each source is a Poisson for each source is exponentially distributed with parameter
k
process). Now consider the arrival stream, which is formd by merging the input from each of the K sources defined above. Prove that this merged stream is also Poisson with parameter K λλλλ+++= 21.
Solution ：证明见幻灯片，用归纳法证明。
2.2 Referring back to the previous problem, consider this merged Poisson stream and now assume that we wish to break it up into several branches. Let p i be the probability that a customer from the merged stream is assigned to the substream i. if the overall rate is λ customers per second, and if the sub stream probabilities p i are chosen for each customer indepencently, then show that each of these sub streams is a Poisson process with rate i p λ.
Solution ：证明见幻灯片，用归纳法证明。
2.3 Let {X j } be a sequence of identically distributed mutually independent Bernoulli random variables (with P[X j =1]=p, and P[X j =0]=1-p). Let S N =X 1+…+X N be the sum of a random number N of the random variables X j , where N has a Poisson distribution with mean λ. Prove that S N has a Poisson distribution with mean p λ . (In general, the distribution of the sum of a random number of independent random variables is called a compound distribution)
Solution ：
[]
()()()
()
()()!
!
1!!1!!1!1000m p e e m p e p k m p e p m k m p e p p C k e m S P m p p m m k k k m
m k m
k k m
k m k m m k k N λλλλλλλλλλλλ---∞=-∞=--∞
=--=⋅=-=--=-==∑∑∑
因此S N 服从均值为p λ的Poisson 分布。