Solutions.Assignment #2.FIN 4310.Spring.2016
Assignment_2_Solutions
Chapter 2: Term Structure of Interest Rate1. Song: page 31, #1Answer:(1) If we assume that the coupon is paid annually,For T-Bills: We have r n P n 121100＋=, so: 1-month: r 1211100653.99+=, r = 4.178%; 3-month: r 1231100866.98+=, r = 4.588% 6-month: r 1261100766.97+=, r = 4.570%; 1-year: r +=1100666.95, r = 4.530% For T-Bonds and T-Notes :We have n n n n n n n n n r i r i r i r i P )1(100)1()1(111221+++++++++=-- , so 1)1(110011-+⨯-+=∑-=n n t t t n n nn r i p i r ,We have already known that r 1 = 4.530%, so we can calculate other zero rates by Excel: 2-year: r 2 = 4.522%;3-year: r 3 = 4.532%;4-year: r 4 = 4.551%;5-year: r 5 = 4.562%;6-year: r 6 = 4.624%;7-year: r 7 = 4.571%;8-year: r 8 = 4.632%;Since there ’s no available information for the values from r 9 to r 19, we should use linear interpolation to determine them. The formula is )(n m n j r r nm n j r r ---+=, where n = 8, m = 20, r 8 = 4.632%, so: 9-year: r 9 =2020121%2463.4%)632.4(82089%632.4r r +=---+; 10-year: r 10 = 2061%8603.3r +;11-year: r 11 = 2041%4742.3r +; 12-year:r 12 = 2031%0882.3r +; 13-year:r 13 = 20125%7022.2r +; 14-year:r 14 = 2021%3162.2r +; 15-year:r 15 = 20127%9301.1r +; 16-year:r 16 = 2032%5441.1r +; 17-year:r 17 = 2043%1581.1r +; 18-year:r 18 = 2065%7721.0r +; 19-year: r 19 = 201211%386.0r +;。
Assignment_8_for_2010_Solutions
201Tutorial8/Marked Assignment22010 topic:Static gameshand in date:day21Monday24Mayreading:Perloffchapters13,14Q1Chewing guma)Twofirms,A and B,compete in the chewing gum industry.Theproducts of the twofirms are differentiated.The demand functionsfor the products of thesefirms are Q A=120−2P A+P B and Q B=120−2P B+P A,where the subscript denotes thefirm.Eachfirm haszero production costs.(a)Suppose that the twofirms play a Bertrand game.Write downthe objective function forfirm A.The profit offirm A isπA=P A Q A=(120−2P A+P B)P A.(b)Assume that prices can only be set in tens,with a maximum of50.The following matrix gives the payoffs possible values of A’sprice(rows)and B’s price(columns).Firm A’s payoffs are givenfirst.Identify(i)the best responses with the circling method and(ii)the Nash equilibrium.150015002500330035003500 402400240032003200210013002700270033002500 2020002000240024001100110013002100150015002040Firm A’s best response is indicated with bold payoffs in thefollowing table.1Moreover,the game is symmetric,so we mightexpect the equilibrium to feature both players choosing the sameprice.Cells in which both players choose the same price areindicated with payoffs in italics.Consequently,the symmetricNash equilibrium has a bold and italicised payoff,ie.with bothfirms choosing a price of$40.1500250035002000280036002100270033001800220026001100130015002040(c)Now assume that prices can be any nonnegative real number.Take afirst-order condition and use it tofind the best-response function of eachfirm.Firm A’s optimal price satisfies thefirst-order condition∂πA.Similarly,firm B’s reaction4function is P B=120+P Ax 2be the location of Firm 2.Assume that the location decisions are made simultaneously.The payoffs to the two firms are:π1(x 1,x 2)=12−x 21−(x 2−x 1)2π2(x 1,x 2)=12−(1−x 2)2−(x 2−x 1)2a)Derive best response functions for the two firms.Sketch them in(x 1,x 2)space.MB 1=−2x 1+2(x 2−x 1)=0and MB 2=2(1−x 2)−2(x 2−x 1)=0.So the two best response functions are:B 1(x 2)=x 22.b)Identify the Nash equilibrium.State it and also show it in your dia-gram. x 1=1300.20.40.60.81.000.20.40.60.81.0x 2x 1(x 1)3Q3WarrantiesAcura and Volvo offer warranties on their cars,where w A is the number of years of an Acura warranty and w V is the number of years of a Volvo warranty.The revenue forfirm i,i=A for Acura and V for Volvo,is R i= 27,000w i/(w A+w V).The cost of providing the warranty is C i=2,000w i.Acura and Volvo play a warranty-setting game in which they simultaneously set the length of warranties.2Volvo’s indifference curves are drawn in(w V,w A)space below.a)Sketch Volvo’s best response function into the indifference curve dia-gram.The trick is tofind the point of zero slope of each indifference curveand then connect the dots.You should get a backward-bending best-response for Volvo,as illustrated by the blue curve.Note that thetwo diagrams don’t have the same scale-the second one starts from(1,1)rather than(0,0).In fact the best response goes to(0,0)in thelimit,but it is next to impossible to determine that from looking atthe indifference curve diagram.Unfortunately,I did give them the payofffunctions,so although I amnot expecting or requiring it,some people may attempt a mathemat-ical derivation.If they do,Volvo’s FOC is27w A/(w A+w V)2−2=0.Solving for w V gives the best response function w V=B V(w A)=2Technically,payoffs are undefined when wA=w V=0,so let’s ignore warranties of zero length.4The students haven’t been taught about contract curves,as general equilibrium is no longer in the course.So don’t be distraught if they mostly don’t get this right.1234561 2 3 4 5 627*y/(y+x)2-227*x/(y+x)2-25。
ASSIGNMENT 2 Solutions
E(x2 )
2 2 x f ( x)dx x 2 xdx 0
1
1 41 1 x 0 2 2
ASSIGNMENT 2
1. Three balls are drawn in succession without replacement from an urn containing 2 red balls and 3 black balls. Let W be a random variable giving the number of black balls minus the number of red balls drawn. List the elements of the sample space S for the three draws and to each sample point assign a value w of W. Key: S ●●● ●●● ●●● ●●● ●●● ●●● ●●● W -1 -1 -1 1 1 1 3
3. Consider the density function
2x ke , x 0 f ( x) 0, elsewhere
(a) Find the value of k (b) Find F(x) and use it to calculate P(-0.5<x<-0.2 ). Key:
3 0.1 0.133 0.167
0 X 1 2
(a) (b) (c) (d)
0 0.033 0.067
0.033 0.067 0.1
0.067 0.1 0.133
P( X P( X P( X P( X
1, Y 2) 0.067 0.1 0.167 ; 1, Y 1) 0.033 0.067 0.1 0.067 0.1 0.133 0.5 ; Y ) 0 0.033 0.067 0.1 0.067 0.1 0.133 0.133 0.167 0.8 ; Y 3) 0.1 0.1 0.1 0.3 ;
描写作业的英语
Homework is an essential part of the educational process,designed to reinforce and deepen the understanding of concepts taught in class.It can take various forms,such as written assignments,reading tasks,practical exercises,or research projects.Heres a detailed description of the different aspects of homework in English:1.Purpose of Homework:Homework serves multiple purposes.It helps students to practice and apply the knowledge gained in class,develop time management and organizational skills,and foster a sense of responsibility and selfdiscipline.2.Types of Homework:Written Assignments:These include essays,reports,and problemsolving tasks that require students to write down their thoughts and solutions.Reading Assignments:Students are often asked to read chapters from textbooks or articles to prepare for class discussions or to gain a deeper understanding of a topic. Math Problems:In subjects like mathematics,students are given problems to solve, which helps them to apply mathematical concepts and improve their problemsolving skills.Science Experiments:Sometimes,students are asked to conduct experiments at home or in the lab to explore scientific concepts further.Research Projects:These are indepth assignments where students are expected to explore a topic extensively,gather information,and present their findings.3.Homework Guidelines:Teachers usually provide guidelines for completing homework, which may include due dates,formatting requirements,and the level of detail expected in the answers.4.Strategies for Effective Homework:Time Management:Allocating specific times for homework can help students stay organized and avoid lastminute rushes.Study Groups:Collaborating with classmates can provide different perspectives and make the learning process more enjoyable.Asking for Help:If students are struggling with their homework,its important to seek help from teachers,tutors,or peers.5.Technology in Homework:With the advent of digital tools,homework can now be completed using computers,tablets,or smartphones.Online platforms and educational apps provide interactive ways to complete assignments and receive feedback.6.Homework and Learning Outcomes:Research has shown that homework can improve academic performance when assigned in a thoughtful and balanced manner.However,excessive amounts of homework can lead to stress and burnout.7.Homework Challenges:Procrastination:Many students struggle with putting off homework until the last minute,which can lead to poor quality work and increased stress.Distractions:The presence of digital devices and social media can make it difficult for students to focus on their assignments.WorkLife Balance:Students need to find a balance between schoolwork and other activities to maintain their mental health and wellbeing.8.Feedback on Homework:Teachers provide feedback on completed homework to help students understand their mistakes and learn from them.This feedback is crucial for academic growth and improvement.9.Homework Policies:Schools and educational institutions may have specific policies regarding homework,including the amount of homework assigned,the frequency of assignments,and the consequences for not completing homework.10.Cultural Perspectives on Homework:Attitudes towards homework vary across cultures.In some countries,homework is considered a necessary part of education,while in others,it may be seen as an unnecessary burden on students.Homework is a critical component of the educational experience,but it must be approached with a balance that respects students time and wellbeing.It should be a tool for learning and growth,rather than a source of undue stress.。
Course Outline
Course Meeting Time and Location:Mondays and Wednesdays, 11:15am - 12:40pmClass meets in room 220 of the Stuart Building (220 SB)Textbook:Chi-Tsong Chen, Linear System Theory and Design, 3rd ed., Oxford University Press, 1999. ISBN: 0-19-511777-8Course Objectives:After completing this course, the student should be able to do the following things correctly: ∙formulate state space descriptions of linear dynamical systems, in both time-invariant and time-varying cases, and for both continuous-time and discrete-time systems;∙find the analytic solution of state equations and give a geometric interpretation of the state space in terms of the system dynamics;∙apply the concepts of stability, controllability and observability in interpreting and analyzing system behavior;∙formulate input-output descriptions of linear dynamical systems, in both time-invariant and time-varying cases, and for both continuous-time and discrete-time systems;∙construct realizations of input-output system descriptions via state space system dynamics;∙use state feedback to reshape system dynamics;∙use observers to infer knowledge of the system states given input and output measurements;∙use computer-based analysis and design tools (such as {\sc Matlab} software) in the analysis of linear, time-invariant systems.Course Documents:These documents are available in pdf or html format.∙Course syllabuso Syllabus as an html documento Syllabus as an Excel document∙Suggested additional references∙The Kalman Decomposition: a document describing how to find the coordinate transformation leading to the Kalman decomposition and giving an example of theapproach.Homework Policy and Assignments:Please follow these rules when submitting homework papers. Any exceptions to these basic policies should be confirmed with the instructor before submitted your paper.∙Use 8 1/2 x 11 inch or A4 paper (other sizes are not accepted), with multiple pages stapled together in the upper left corner. Do not use any means other than stapling tohold pages together (in that event, the grader has full authority to discard all but the first page).∙Your homework paper should present answers to the questions in the same order that they appear in the assignment. At the grader's discretion, zero credit may be given forwork the appears out of order.∙No email submissions are accepted unless prior arrangements have been made due to special circumstances, or unless the assignment specifically requests email submission.∙No late homeworks will be accepted without prior approval by the instructor. (Generally, approval of late homework submission requires there to be very extenuatingcircumstances. I drop the lowest homework score in part to accommodate the commonsituations that prevent persons from completing the assignments on time.)Homework assignments, when available, will be posted here in pdf format.∙Assignment #1 [posted 26 Jan 2007] (due 7 February 2007) [Note the new (later) due date!]∙Assignment #2 [posted 7 Feb 2007] (due 14 February 2007)∙Assignment #3 [posted 14 Feb 2007] (due 28 February 2007)∙Assignment #4 [posted 13 Mar 2007] (due 28 March 2007) [Problem #1 typo corrected15 Mar 2007]o Here are a couple of supplementary problems for controllable and Kalman decompositions that are non-degenerative (unlike problems 4 and 5 on HomeworkAssignment \#4). For your convenience the various system matrices are stored inthe file hw4_supp_data.mat. To access the variables, save this file to yourcomputer, and change the working directory of Matlab to the directory where yousaved the file (or alternatively add that directory to Matlab's path). You then loadin the system matrices by typing "load hw4_supp_data" at the Matlab prompt.▪Assignment #4 supplement▪hw4_supp_data.mat∙Assignment #5 [posted 26 Mar 2007] (due 13 April 2007, on-campus students please submit homework by putting it in my mailbox in the ECE Department; off campusstudents may submit homework in the usual way)∙Assignment #6 [posted 12 Apr 2007] (due 25 April 2007)Homework Solutions:Homework solutions will be posted either here or at the Galvin Library's Electronic Reserves.∙Solutions to Assignment #1 [submitted for posting at the Galvin Library's Electronic Reserves on 7 Feb 2007 and posted there on 8 Feb 2007]∙Solutions to Assignment #2 [submitted for posting at the Galvin Library's Electronic Reserves on 14 Feb 2007 and posted there on 15 Feb 2007]∙Solutions to Assignment #3 [submitted for posting at the Galvin Library's Electronic Reserves on 28 Feb 2007 and posted there on 1 Mar 2007]o ECE531_07S_hw3_p3.m: Matlab m-file for problem 3 of Assignment #3 (save to your own computer and run from there)∙Solutions to Assignment #4 [submitted for posting at the Galvin Library's Electronic Reserves on 28 Mar 2007 and posted there on 28 Mar 2007]∙Solutions to Assignment #5 [submitted for posting at the Galvin Library's Electronic Reserves on 16 Apr 2007 and posted there on 17 Apr 2007]∙Solutions to Assignment #6 [submitted for posting at the Galvin Library's Electronic Reserves on 25 Apr 2007 and posted there on 26 Apr 2007]Examinations:There will be two take-home examinations during the course of the term, and one in-class final examination. The take-home examinations, when available, will be posted here in pdf format.∙Take-home Exam #1 (due 7 March 2007 at 11:25am) [Problem 8 corrected on 2 March 2007 to include a missing transpose.]o Solutions to Take-home Exam #1 [submitted for posting at the Galvin Library's Electronic Reserves on 22 Mar 2007 and posted there on 23 Mar 2007] ∙Take-home Exam #2 (due 2 May 2007 at 11:25am)o Solutions to Take-home Exam #2 [submitted for posting at the Galvin Library's Electronic Reserves on 7 May 2007 and posted there on 7 May 2007]. Note: theproblem 2 solutions shown here are for a problem not on the exam. The problem 3solutions solve problem 2 on the exam. The problem 4 solutions solve problem 3.Problem 4's solutions are missing, but are included in the supplement.o Supplement to solutions to Take-home Exam #2 [submitted for posting at the Galvin Library's Electronic Reserves on 7 May 2007 and posted there on 7 May2007]. These are the missing problem 4 solutions.∙In-class final examination: Wednesday, 9 May 2007, 2:00 - 4:00pm∙Sample in-class examinations are available as follows:o Final Exam, Spring 2001o Final Exam, Spring 2002o Final Exam, Spring 2004o Final Exam, Spring 2005o Final Exam, Spring 2006Grading:∙Homework: 20% (best 5 of 6 assignments)∙Take-home Exam #1: 30%∙Take-home Exam #2: 30%In-class Final: 20% (the final is comprehensive)Academic Honesty:It is your responsibility to be familiar with IIT's Code of Academic Honesty. (Consult the IIT Student Handbook for this code.)In particular, the work that you submit for homework and individual project assignments and your work on examination papers must be your own. You may consult with other students about homework and project assignments. In fact, discussion of the assignments is encouraged. However, the written material that is submitted must be your own. Such written material includes computer programs and the results of using computer programs (computed values, plots, etc.). If the above policy or any part of IIT's Code of Academic Honesty is violated in regard to a submitted homework assignment, a grade of zero will be assigned to the work. If the above policy or any part of IIT's Code of Academic Honesty is violated in regard to a submitted project assignment or an examination paper, a punitive failing grade will be given in the course. In both cases, the matter will be reported to the appropriate university officials and offices. In the case of a second offense (with the first offense in this or any other course), expulsion from the university will be advocated.。
assignment_completed
Online Gaming regulations are in emergencySubmission to the Australian Government on theRevision of Interactive Gaming Act 2001[Name of student][Student ID]For [Instructor Name]This assignment is approximately 1643 words in lengthContentsIntroduction to the Australian Council of Social Services (3)Problem Gambling (3)History of online gaming (3)Recent Developments (4)Online gaming is the major source of problem gambling (4)Problem gambling caused various social issues (5)Financial impacts from online gaming (6)Conclusion (6)References (8)Introduction to the Australian Council of Social ServicesThe Australian Council of Social Service (ACOSS) is the national-wide body of the community services and welfare sector. Founded in 1956, ACOSS aims to reduce poverty and inequality by promoting public policies and actions by government, community and private sectors towards socially and environmentally responsible. ACOSS supports non-government organizations which provides assistance to the general public and contributes to national public policy design.Problem gamblingThe term "Problem Gambling", according to the website , is …used to describe gambling behavior, which causes disruption in any important life function, whether psychological, physical, social or vocational. This term is generally accepted to include, but is not limited to "Pathological", a.k.a., "Compulsive" gambling. Compulsive Gambling is a progressive addiction characterized by increasing preoccupation with gambling, a need to bet more money more frequently, restlessness or irritability when attempting to stop gambling, "chasing" losses, and loss of control by continuing negative gambling behavior, regardless of the disruption and serious consequences of such behavior.‟ (, 2009)History of online gamingThe history of online gambling is quite short. Online gaming started in the 1990's and has become explosive ever since. Internet betting has become a multi-billion dollar industry in a very short time and its size, in fiscal sense, is still having a rapid growth. The catalyst for the rapid growth happened in 1994, when the government of the Caribbean island, Antigua Barbuda, passed the law that enables online casinos to operate from their homeland to this day - the Free Trade and Processing Zone Ac t. Australia grants the first and only online casino license to Lasseters. By the year 2000, the Federal Government of Australia put into effect the Interactive Gambling Moratorium Act, which prohibits any online casino or sportsbook formed after May of 2000 to operate domestically.Recent developmentsIn June 2010, Australian Productivity Commission (PC) has published a report to recommend that online gambling has to be legalized, regulated, and taxed. Responding to a request from the Australian government, the PC has updated their 1999 inquiry into the gambling industry and has returned a report to the federal government. The report makes a large number of recommendations. The government is under no obligation to accept their recommendations of the Productivity Commission, but is likely to take its comments very seriously. Since thepublication of the report, the issue of limiting online gaming has been the center of some heated media attention in the past few monthsOnline gaming has gained wide acceptance and popularity among gamblers for its convenience. An estimated 20 million people worldwide gamble online at internet casinos. In 2007, Americans spent $34 billion on gambling in bricks and mortar casinos, and that number does not include the amount spent at Native American casinos. In the case of Australia, the revenue from online gaming grows at an annual rate of 3.5% in the past decade despite the fact that some traditional gaming places have shown zero or negative growth rates over the same period.This submission addresses the concerns of limiting online gaming. Various researches have shown that online gaming is a catalyst to problem gaming. Problem gambling is ten times more common among those who gamble online than among those who only gamble offline, according to the research conducted by Griffiths (2007). The PC also suggested in the report that these computerized gambling machines account for 80% of problem gambling in Australia.Online gaming catalyzes problem gamblingThe medium of the internet may be more likely to contribute to problem gambling than gambling in offline environments. Problem gamblers and those at risk contribute a significant portion of Australian electronic gaming machine spending.Despite the fact that the cause of gambling problem is the individual‟s ability to control the gambling, anecdotal reports indicate that one risk factor may be a fast speed of play. In other words, the faster the wager to response time with a game, the more likely players may be to develop problems with a particular game. With the advance of technology and the spread of the Internet throughout the last decade, it becomes faster and more convenient for gamblers to access online gaming portals.Liberal online gaming has made the situation worse. Inadequate protection from the existing IGA does not help in improving problem gaming in Australia as consumption by Australians of electronic gaming machines increases.Researches have also found that a higher portion of online gamblers are classified as “problem” or “pathological” gamblers, compared to people who visit conventional land-basedcasinos. Besides, online gambling is even more addictive than ordinary live gambling, since internet in itself has an addictive effect on individuals.Problem gambling caused various social issuesA recent research study was done by the National Opinion Research Center at the University of Chicago, in collaboration with three other research bodies. Gestian et al (1999) reported that …based upon criteria developed by the American Psychiatric Association, we estimate that about 2.5 million adults are pathological gamblers and another 3 million adults should be considered problem gamblers.‟Take the state of Victoria as an example, problem gamblers in Victoria have been found to spend nearly three times the amount spent by non-problem gamblers ($A103 versus about $A36), and to make six times as many visits to automatic teller machines (ATMs) (Caraniche Pty Ltd 2005). Problem gamblers spent around six times as much as non-problem gamblers, a total of $A443 per week or over $A23,000 annually. Problem gamblers were estimated to spend about nineteen-folds of recreational gamblers on average.With the current IGA, Australia has the highest percentage of problem gamblers among major developed countries, according to a survey. Applying the same methodology used in the report published by Sproston et al (2000), approximately 2.3% of population in Australia are problem gamblers. This is significantly higher than the international average of 1.5%.Various studies have found high rates of alcoholism, depression, anti-social personality disorder, mood disorders, and other conditions in pathological gamblers, leading some researchers to suspect that problem gambling is often a symptom of an underlying condition.Financial impacts from online gamingPromotion of online gaming impacts revenue of traditional gaming. Despite a strong growth in revenue, online gambling, on the one hand, is only responsible for 4% of all national gaming. The revenue generated from online gaming is not the major portion of total gaming revenue. Moreover, there are studies concluding that total revenue from gaming industry may not be necessary increased with the introduction of more online gaming machines. According to national statistical bureau, the revenue growth of conventional gaming showed a negative trend after additional online gaming machines have been set up.Problem gamblers have highly likelihood to experience adverse consequences such as broken relationships and families and alcoholism. Although the economic costs of these consequences cannot be measured directly, there are other tangible economics costs that are usually spread around the community. Earlier studies found out problem gamblers experienced higher rates of personal bankruptcy and higher divorce rates. (Volberg 1998). For instance, according to Gestian et al, (1999) in the United States, …problem gambling costs the society approximately $5 billion per year and an additional $40 billion in lifetime costs for productivity reductions, social services, and creditor losses. However, these calculations are inadequate to capture the intra-familial costs of divorce and family disruption associated with problem and pathological gambling.‟The public does necessarily enjoy the taxation levied from online gaming. Electronic gaming machine operators are not required to be registered in Australia and therefore tax levied on conventional gaming is not applicable to online gaming. However, problem gamblers have caused additional resources from the community for its social problems. It is clear that the costs of liberal online gaming outweigh the benefits.ConclusionThis submission has presented the evidence that supports stricter regulation of online gaming, in addition to the existing IGA. Reviewing the existing IGA is not sufficient. Our recommendation is simple: impose limits in online gaming. The effects of problem gambling are well documented and the financial costs of problem gambling cannot be ignored and should be addressed seriously. Prompt actions have to be taken to promote an effective regulatory regime to address online gaming. Gaming is a vital industry in Australia and its contribution to the economy should be well perceived. The government has its obligation to promote a sustainable development for the gaming industry and balance the impacts of online gaming.ReferencesGriffiths M. et al (2009), Sociodemographic Correlates of Internet Gambling: Findings from the 2007 British Gambling Prevalence Survey, CyberPsychology & Behavior., Vol. 12, No. 2: 199-202.Young, C. (2007) Frequently Asked Questions on problem gambling, [Online], Available: /faq.html, Date accessed 22/9/10.Sproston, K. et al (2000) Results from the British Gambling Prevalence Survey, London: National Centre for Social Research.Delfabbro, P.H. & Winefield, A. H. (1999), …Poker-machine gambling: An analysis of within-session characteristic s’, British Journal of Psychology, 90, 425-439.Griffiths, M. (1999), …Gambling technologies: Prospects for problem gambling.‟Journal of Gambling Studies, 15(3), 265-283.Williams, R et al (2005), W hat Proportion of Gambling Revenue is Derived from Problemth Gamblers. presentation at the European Association for the Study of Gambling (EASG), 6 European Conference, Malmo, June 29 – July 2.Caraniche Pty Ltd, (2005). Evaluation of Electronic Gaming Machine Harm minimisation Measures in Victoria. Department of Justice, Melbourne. Print.Livingstone, C. et al (2008). The Relevance and Role of Gaming Machine Games and Game Features on the Play of Problem Gamblers.Independent Gambling Authority, South Australia. .au/pdf/0801/Final%20report.Print.Feb08.pdfGerstein, D. et al (1999). Gambling Impact and Behavior Study. Natioanl Gambling Research Center./dlib/ngis.htm。
Assignment_1_suggested_solutions
Speaking of Statistics(12) - Assignment 1 – Suggested Solution1. Below we list several variables. Which of these variables are quantitative and which arequalitative? Explain.a. The dollar amount on an accounts receivable invoice. → Quantitativeb. The net profit for a company in 2005. → Quantitativec. The stock exchange on which a company’s stock is traded. → Qualitative d. The national debt of the United States in 2005. → Quantitativee. The advertising medium (radio, television, or print) used to promote a product. → Qualitative2. Classify each of the following qualitative variables as ordinal or nominative. Explain youranswers.Qualitative Variables The Corresponding CategoriesStatistics course letter grade A B C D F →Ordinal Personal computer ownership Yes No → Nominal Restaurant rating ***** **** *** ** * → Ordinal Incoming tax filing status Married filing jointly; Married filing separately; Single; Headof household; Qualifying widow(er) → Nominal3. Forbes magazine publishes the Forbes Platinum 400 –a list of the ―Best Big Companies inAmerica‖ as selected by the magazine’s writers and editors. Table above gives the best companies in the retailing industry as given in this list on the Forbes website on March 16, 2005. (Data in the last page ).b. Organize data of the profit margin percentages into a frequency distribution.Number of class K=6 (Since n K≥2 where n is the total number of data = 35.) The class length is calculated as 9.381.361.10.24≈=-=K rangea. Construct a stem-and leaf display of the return on capital percentages for the retailers in Table.Find the median and then describe the distribution of the return.The median is the 18th measurement, 15.4.The data are widely spread out, with majority falling in the range [8.3, 22.8]. The distribution is somewhat symmetric, with extreme values at both ends.c.Construct a histogram of the profit margin percentages.4. In order to control costs, a company wishes to study the amount of money its sales forcespends entertaining clients. The following is a random sample of six entertaining expenses (dinner costs for four people) from expense reports submitted by members of the sales force $157 $132 $109 $145 $125 $139a. Show the equivalence of the following two formulas:,.Solutions:()⎥⎦⎤⎢⎣⎡--=⎥⎥⎦⎤⎢⎢⎣⎡⎪⎪⎭⎫ ⎝⎛+--=++++++-+++-=+-+++-++--=-++-+--=--=--=∑∑∑∑∑∑∑∑22222221222212222222121222212221 1 1)(2(11)]...()2...22()...[(11)]2(...)2()2[(11])(...)()[(11)(111)(i i i i i i n n n n n i ix n x n n x n x n x x n x x x x x x x x x x x n x x x x x x x x x x x x n x x x x x x n x x n n x x sb. Calculate x , 2s , and s for the expense data, use the two different formulas in (a) to calculate 2s .Solutions 5.1346139125145109132157=+++++=x7.27616)5.134 139()5.134 132()5.134 157(2222=+++= s , 63.167.276==sOr using another formula:925,1091391251451091321572222222=+++++=∑ix()249,651)807()139125145109132157(222==+++++=∑ix()⎥⎦⎤⎢⎣⎡--=∑∑2221 1 1i i x n x n s 7.276)249,651(61–925,1091–61=⎥⎦⎤⎢⎣⎡=5. On February 15, 2005, the Gallup Organization released the results of a Gallup UK poll regarding Internet usage in Great Britain. Each of 1,009 randomly selected UK adults was asked to respond to the following question:How much time, if at all, do you personally spend using the Internet-more than an hour a day, up to one hour a day, a few times a week, a few times a month or less, or never?The poll’s results were as follows: More than an hour a day (22%); Up to an hour a day (14%);A few times a week (15%); A few times a month or less (10%); Never (39%). Use these datato construct a bar chart and a pie chart.Bar Chart:Pie Chart:6. Thirteen internists in the Midwest are randomly selected, and each internist is asked to report last year’s income. The incomes obtained (in thousands of dollars) are127 132 138 141 144 146 152 154 162 171 177 192 241 Find:There are 13 measurements in total (n=13). They are already in ascending order. a. The 90th percentile.Calculate the index of the 90thpercentile: 7.111310090=⨯=i Round 11.7 up to 12, hence the 90th percentile is the 90th measurement 192.b. The median.The median is equivalent to the 50thpercentile: 5.61310050=⨯=i Round 6.5 up to 7, hence the median is the 7th measurement 152.c. The first quartile.We know the index of the first quartile can be found as: 25.31310025=⨯=i Round 3.25 up to 4, hence the first quartile is the 4th measurement 141.d. The third quartileWe know the index of the third quartile can be found as: 75.91310075=⨯=i Round 9.75 up to 10, hence the third quartile is the 10th measurement 171.e. The 10th percentile.Calculate the index of the 10thpercentile: 3.11310010=⨯=i Round 1.3 up to 2, hence the 10th percentile is the 2nd measurement 132.f. The interquartile range.Interquartile range is the difference between first and third quartile3014117113=-=-=Q Q IQRg. Develop a five-number summary and a box-and-whiskers display.7. According to the website, the 2004 total return percentages for several popular funds were as follow:Fund 2004 Total Return% Vanguard 500 Index 10.7Wasatch Core Growth 21.7 Fidelity Stock Selector 9.9 Fidelity Dividend Growth6.0Janus Worldwide 5.2Suppose that an investor had $100,000 invested in the Vanguard 500 Index fund, $500,000 invested in the Wasatch Core Growth fund, $500,000 invested in the Fidelity Stock Selector fund, $200,000 invested in the Fidelity Dividend Growth fund, and $50,000 invested in the Janus Worldwide fund.a. Compute a weighted mean that measures the 2004 average total return for the investor ’s portfolio.Compare your weighted mean with the un-weighted mean of the five total return percentages. Explain why they differ.The weighted mean is%56.13000,350,1000,305,18000,50000,200000,500000,500000,100)5.5(000,50)8.5(000,200)9.9(000,500)7.21(000,500)7.10(000,100==++++++++=μAnd the un-weighted mean is%72.1055.58.59.97.217.10=++++The average total return calculated using weighted mean is higher because more money was invested in funds with larger gains, such as Wasatch Core Growth.8. As given on the Morningstar website, the mean return for Fidelity Leveraged Company Stock is 17.98 percent with a standard deviation of 10.02 percent, while the mean return for Baron Opportunity Retail Stock is 16.43 percent with a standard deviation of 12.23 percent. Which stock do you buy? (Which is riskier than the other one?)The mean return for Fidelity Leveraged Company Stock is higher than of Baron Opportunity Retail Stock.When we compute and compare the coefficient of variation for these two stocks using 100mean deviationstandard ⨯ , we find that the coefficient of variation of Fidelity Leverage(73.5510017.9810.02=⨯) is lower than the one of Baron Opportunity (44.7410016.4312.23=⨯), meaning the variation in returns for the Baron Opportunity is higher, so investing in Baron Opportunity is riskier.Therefore investing in Fidelity Leveraged Company Stock is more advisable.9. The card game of Euchre employs a deck that consists of all four of each of the aces, kings, queens, jacks, tens, and nines (one of each suit —clubs, diamonds, spades, and hearts). Find the probability that a randomly selected card from a Euchre deck isThere are a total of 24 cards (4 aces, 4 kings, 4 queens, 4 jacks, 4 tens and 4 nines.a. A jack (J)The probability of selecting a jack is ()61244==J P b. A spade (S)The probability of selecting a spade card is 41246)(==S P c. A jack or an ace (A)The probability of selecting a jack OR an ace is()()()()3106161=-+=⋂-+=⋃A J P A P J P A J P d. A jack or a spade.The probability of selecting a jack OR a spade card is()()()()832414161=-+=⋂-+=⋃S J P S P J P S J P e. Are the events J and A mutually exclusive? J and S? Why or Why not?The events J and A are mutually exclusive because one cannot draw a Jack AND an Ace at the same time in one single draw.The events J and S are NOT mutually exclusive because one can draw a jack of spade under one single draw, hence J and S could occur simultaneously.10. Fifteen percent of the employees in a company have managerial positions, and 25 percent of the employees in the company have MBA degrees. Also, 60 percent of the managers have MBA degree.a. What proportion of employees are managers and have MBA degrees. 9% of employees are managers AND have MBA degrees09.0)6.0)(15.0()|()()(===⋂Manager MBA P Manager P MBA Manager Pb. What proportion of MBAs are managers. 36% of MBAs are managers36.025.009.0)()()|(==⋂=MBA P MBA Manager P MBA Manager Pc. Are the events being a manager and having an MBA independent? Justify your answer.No. Because 15.0)(36.0)|(=≠=ManagerP MBA Manager P11. In a survey of 100 insurance claims, 40 are fire claims (FIRE ), 16 of which are fraudulent (FRAUD ). Also, there are a total of 40 fraudulent claims. a. Construct a contingency table summarizing the claims data. Use the pairs of events FIRE and FIRE , FRAUD and FRAUD .Contingency Table:FireFIRETotal Fraud 16 24 40 Fraud 24 36 60Total4060100b. What proportion of the fire claims are fraudulent? 40% of the fire claims are fraudulent4.04016)()()|(==⋂=Fire P Fire Fraud P Fire Fraud Pc. Are the events a claim is fraudulent and a claim is a fire claim independent? Use your probability of part b to prove your answer. Yes. Because10040)(4.0)|(===Fraud P Fire Fraud P12. Each month a brokerage house studies various companies and rates each company’s stock as being either ―low risk‖ or ―moderate to high risk.‖ In a recent report, the brokerage house summarized its findings about 15a.The probability that the company’s stock is moderate to high risk giventhat the firm is an aerospace company.P(ModToHigh | Areo) = 9/15=0.6b.T he probability that the company’s stock is moderate to high risk giventhat the firm is a food retailer.P(ModToHigh | Food) = 10/25=0.4c.Determine if the company type is independent of the level of risk of thefirm’s stock.If the company type is independent of the level of risk of the firm’s stock, the we should find equalities such asP(Aero | Low) = P(Aero)However, P(Aero | Low) = 2/7 while P(Aero) = 3/8.The two probabilities are not equal. Hence the two events are dependent.Table for question 3:The Forbes platinum list: Best-performing retailers as listed at on March 16, 2005。
assignment1-solution
Operations ResearchLecture 0: Assignment 1Notes taken by Kaiquan XuDue Date: October 18th 20121Assignment DescriptionGiven a manufacturer plans to produce two types of products: I and II, the required matireials (A & B) and equipment for producting one product are list in Table 1. The profits for Product I and II are 2$ and 3$.The question is: how to make product planning, so the manufacturer can get the maximum profit.1)Please write this problem as a linear programming problem (10 marks).2)Try to draw the graphical representation and find its solution (10 marks).3)Try to use the simplex method to find its optmial solution (30 marks).4)Try to write its dual problem (15 marks).5)2Solution1)Please write this problem as a linear programming problem (10 marks)Let x1and x2be as the numbers of Product I and II to be produced. Under the constraints of the resources, the variables should satisfy the following conditions:x1 + 2x2≤84x1≤164x2≤12The profit z can be represented as z = 2x1 + 3x2. This problem can be described as the following math model:max z = 2x1 + 3x2s.t. x1 + 2x2≤ 84x1≤ 164x2≤ 12x1, x2≥ 012B − − u i u 2) Try to drop the graphical representation and find its solution (10 m arks) (skip)3) Try to use the simplex method to find its optmial solution (30 marks)Transform this problem into the standard formmin 2x 1 3x 2s.t. x 1 + 2x 2 + x 3 = 8x 1 + x 4 = 4 x 2 + x 5 = 3x 1, x 2, x 3, x 4, x 5 ≥ 0It is obvious that x = (0, 0, 8, 4, 3)T is a basic feasible solution. That is x 3, x 4, x 5 are as the basic variables, then the 1 0 0corresponding basis matrix B = 0 1 0 , c B = 0, therefore c T B = 0 and c = c .0 0 1x 1 x 2 x 3 x 4 x 5 0-2 -3 0 0 0 x 3 = 8 1 2 1 0 0 x 4 = 4 1s 0 0 1 0 x 5 = 31 0 0 1The reduced cost of x 1 is negative and we let that variable enter the basis. The pivot column u = (1, 1, 0)T , andcaculate the ratios x B (i ), i = 1, 2, the smallest ratio corresponds to i = 2. We select x 4 to exist the basis. Then x 3, x 1, x 5 are the new basic variables. Then we do some row operations to get the new tableaux 1 x 2 x 3 x 4 x 5 80 -3 0 2 0 x 3 = 4 0 2∗ 0 -1 0 x 1 = 4 1 0 0 1 0 x 5 = 31 0 0 1The corresponding basic feasible solution is x = (4, 0, 4, 0, 3)T . x 2 has negative reduced cost, we choose x 2 to theone that enter the basis. The pivot column is u = (2, 0, 1)T . We only caculate the ratioes x B (i ), for i = 1, 3. We select i x 3 exist the basis, then execute the row operations.x 1 x 2 x 3 x 4 x 5 14 0 0 0 1/2 0 x 2 = 2 0 1 0 -1/2 0 x 1 = 4 1 0 0 1 0 x 5 = 10 0 1/2 1Now, all reduced costs are nonnegative. We get the optimal solution 4) Try to write its dual problem (15 marks)The dual of this problem ismax 8p1 + 4p2 + 3p3s.t. p1 + p2≤ −22p1 + p3≤−3p1≤0p2≤0p3≤05)Since x∗1 >0and x∗2 >0,we havep1 + p2 = −22p1 + p3 = −3By solving this equations, we get p1 = −3/2, p2 = −1/2, p3 = 0, which is a dual optimal solution. Here, the simplex method for the dual problem is skipped.3。
assignment英语解释
Assignment是英语中的一个词汇，它有着多种不同的含义和用法。
在本文中，我们将对assignment的含义进行深入解释，涵盖其在日常生活和学术领域中的各种使用情况。
一、assignment的基本含义1. 在日常生活中，assignment指的是任务、工作或者指定的事项。
这可能是工作上的任务，也可能是家庭中分派的责任或者职责。
老师布置的作业就可以称之为assignment，家长交代的家务任务也可以看作assignment。
2. 在学术领域中，assignment通常指的是老师或者导师布置的作业、论文或者项目任务。
学生需要完成这些assignment并按时提交，以展示他们对所学知识的理解和掌握程度。
二、assignment在学术领域中的更多用法1. assignment作为学术用语，一般指的是教师布置的作业或者课程任务。
这些assignment可以是书面作业、口头报告、实验报告等形式。
2. 不仅仅在学校教育中，assignment也常常出现在大学、研究机构等教育和科研领域。
研究生可能需要完成导师布置的assignment，如完成某项实验、撰写研究报告等。
3. 在商学院和管理学院中，assignment可能指的是实际案例分析、行业调研、商业计划等实践性的任务。
4. 另外，assignment还可以是指派某项任务或者角色。
比如在学生小组中，老师可能会指定每个学生的任务或者角色，这也可以称之为assignment。
三、assignment的重要性1. 在学术领域中，assignment是对学生学习成果的一种评估方式，也是学生掌握知识和技能的重要途径。
通过完成assignment，学生可以巩固所学的知识，提高解决问题的能力。
2. 对于教师来说，布置assignment也是一种教学手段，可以检验学生对课程内容的理解和掌握情况。
通过assignment，教师可以及时发现学生存在的问题和困难，并加以帮助和引导。
ecm06-hw1-solutions
Winter 06
Econometrics
ASSIGNMENT 1 - SOLUTIONS
100 POINTS TOTAL
DUE: Thursday, January 26, 3:20 p.m.
1. [5] Let X be the random variable distributed as Normal (5,4). Find the probabilities of the following events: (i) P(X ≤ 6) (ii) P(X > 4) (iii) P(|X – 5| > 1) (i) P(X ≤ 6) = P[(X – 5)/2 ≤ (6 – 5)/2] = P(Z ≤ .5) [We obtain P(Z ≤ .5) from Table 1.]
trivial solutions的意思
trivial solutions的意思
"trivial solutions"是一个数学术语，用于描述在解决方程或问题时，显得非常简单和显而易见的解决方案。
这些解决方案通常是在问题中所给的条件或约束下可以轻松得出的结果。
在数学中，一个问题可能有多个解，其中一些解是非常特殊或平凡的，也就是所谓的"trivial solutions"。
这些解可能是显而易见的，或者是通过简单的代数运算即可得到的。
举例来说，考虑一个一元二次方程aa^2 + aa + a = 0。
其中a、a和a是已知的常数。
当a=0时，方程变成了一个一次方程，解可以直接通过代数运算得到。
这样的解被认为是"trivial solution"，因为它很容易得到且不需要复杂的数学推理。
另一个例子是在线性方程组中找到"trivial solutions"。
考虑一个由多个线性方程组成的方程组，如果所有的未知数都等于零时，方程组成立，这也是一个"trivial solution"。
因为这个解是显而易见的，不需要进行任何计算。
需要注意的是，尽管"trivial solutions"在数学中通常被认为是简单和显然的解决方案，但在特定的上下文中，它们也可能具有重要的意义。
在某些情况下，"trivial solutions"可能是其他更复杂解的特殊情况或极限情况。
因此，无论是在数学还是其他学科中，理解"trivial solutions"的概念对于全面理解和解决问题都是重要的。
solutions for assignment5
Chapter 5+6+8 AssignmentsP5.Consider the 5-bit generator, G= 10011, and suppose that D has the value 1010101010. What is the value of CRC?Solution:If we divide 10011 into 1010101010 0000, we get 1011011100, with a remainder of R=0100.P21. Suppose nodes A and B are on the same 10Mbps Ethernet bus, and the propagation delaybetween the two nodes is 245 bit times. Suppose A and B send frames at the same time, the frames collide, and then A and B choose different values of K in the CSMA/CD algorithm. Assuming no other nodes are active, can the retransmissions from A and B collide? For our purposes, it suffices to work out the following example. Suppose A and B begin transmission at t =0 bit times. They both detect collisions at t =245 bit times. They finish transmitting a jam signal at t = 245 + 48 = 293 bit times. Suppose K A =0 and K B = 1. At what time does B schedule its retransmission? At what time does A begin transmission? (Note: The nodes must wait for an idle channel after returning to Step 2 -- see protocol.) At what time does A's signal reach B? Does B refrain from transmitting at its scheduled time?Solution:Because A's retransmission reaches B before B's scheduled retransmission time (805+96), B refrains from transmitting while A retransmits. Thus A and B donot collide. Thus the factor 512 appearing in the exponential backoff algorithm is sufficiently large.P23. Suppose four nodes, A, B, C, and D, are all connected to a hub via 10Mbps Ethernet cables.The distances between the hub and these four nodes are 300m, 400m, 500m, and 700m, respectively. Recall that the CSMNCD protocol is used for this Ethernet. Assume that the signal propagation speed is 2*108m/sec.a. What is the minimum required frame length?b. If all frames are 1500 bits long, find the efficiency of this Ethernet.Solution:a). minimum required frame length is given by2*d prop* BW=2*(500+700)/( 2 108) * 10 * 106=120 bits.There is no maximum required packet length.b). Efficiency is given by1/(1+5* d prop/ d trans) =1/(1+5*120/2/1500 )=0.83P37. In this problem, you will put together much of what you have learned about Internetprotocols. Suppose you walk into a room, connect to Ethernet, and want to download a web page. What are all the protocol steps that take place starting from powering on your PC to getting the web page? Assume there is nothing in our DNS or browser caches when you power on your Pc. (Hint: the steps include the use of Ethernet, OHCP, ARP, ONS, TCP, and HTTP protocols.) Explicitly indicate in your steps how you obtain the IP and MAC addresses of a gateway router.Solution:(The following description is short, but contains all major key steps and key protocols involved.)Your computer first uses DHCP to obtain an IP address. You computer first creates a special IP datagram destined to 255.255.255.255 in the DHCP server discovery step, and puts it in a Ethernet frame and broadcast it in the Ethernet. Then following the steps in the DHCP protocol, you computer is able to get an IP address with a given lease time.A DHCP server on the Ethernet also gives your computer a list of IP addresses of first-hop routers, the subnet mask of the subnet where your computer resides, and the addresses of local DNS servers (if they exist).Since your computer’s ARP cache is initially empty, your computer will use ARP protocol to get the MAC addresses of the first-hop router and the local DNS server.Your computer first will get the IP address of the Web page you would like to download. If the local DNS server does not have the IP address, then your computer will use DNS protocol to find the IP address of the Web page.Once your computer has the IP address of the Web page, then it will send out the HTTP request via the first-hop router if the Web page does not reside in a local Web server. The HTTP request message will be segmented and encapsulated into TCP packets, and then further encapsulated into IP packets, and finally encapsulated into Ethernet frames. Your computer sends the Ethernet frames destined to the first-hop router. Once the router receives the frames, it passes them up into IP layer, checks its routing table, and then sends the packets to the right interface out of all of its interfaces.Then your IP packets will be routed through the Internet until they reach the Web server.The server hosting the Web page will send back the Web page to your computer via HTTP response messages. Those messages will be encapsulated into TCP packets and then further into IP packets. Those IP packets follow IP routes and finally reach your first-hop router, and then the router will forward those IP packets to your computer by encapsulating them into Ethernet frames.Additional 1: Please answer the following question after reading Chapter 6 and referring tothe ftp:///chapt6.pdf . What are MAC methods for WiFi, Bluetooth, WiMax and Cellular network respectively? What are RDT approaches for WiFi, Bluetooth, WiMax and Cellular network respectively? error detection + retransmisstion or error correction?Solution:The following table summarizes the wireless MAC and RDT technologies. Each needs to be explained in detail.Additional 2:Why WiFi can’t CSMA/CD?Solution:Because Collisions Detection is difficult for WiFi:∙hidden terminal problem !∙difficult to sense because of fading∙Most radios are half duplexAdditional 3: Please explain how public key cryptography RSA is used in email security protocol: PGP (Pretty Good Privacy). Please refer to Chapter 8Solution:Step 1: Calculate hash (MD5) of message H(m). => you’ve got the digest of the messageStep 2: Encrypt H(m) with Alice’s private key => you’ve got Alice’s signature.Step 3: Append signature to text, then encrypt it with shared key Ks.Step 4: Encrypt shared key Ks with Bob’s public key, then append to the cipher text of step 2 => Bob can get the Ks.Step 5: The result message of step 4 is converted to base64 and be put into an RFC 822 body and be expected to arrive unmodified.D2 (don’t submit) Many of the functions of an adapter can be performed in software that runs onthe node's CPU. What are the advantages and disadvantages of moving this functionality from the adapter to the node?。
sci处理流程待定英语
sci处理流程待定英语English:1. Define the problem.What is the specific problem that you are trying to solve? What are the symptoms of the problem? What are the root causes of the problem?2. Gather data.Collect data from a variety of sources to help you understand the problem. This data can include surveys, interviews, observations, and experiments.3. Analyze the data.Use statistical analysis or other methods to identify patterns and trends in the data. This will help you to identify the key factors that are contributing to theproblem.4. Develop solutions.Brainstorm a variety of possible solutions to the problem. Consider the pros and cons of each solution and select the one that is most likely to be effective.5. Implement the solution.Put the solution into action and monitor its progress. Make adjustments as needed to ensure that the solution is effective.6. Evaluate the solution.Once the solution has been implemented, evaluate its effectiveness. Determine whether or not the problem has been solved and identify any areas where the solution could be improved.Chinese:1. 定义问题。
运筹学：指派问题
Designing School Attendance Zones 设计学生入学区域
米德尔城学区问 题指派问题变形 的电子表格模型
小结
Session Summary 本讲小结
运输问题考虑（确实的或是比喻的）从出发地运送货物到目 的地。每一个出发地都有一个固定的供应量，每一个目的地 都有一个固定的需求量
指派问就要处理应当将哪一项任务指派给哪一个被指派者， 才能使完成这些任务的总达到最小
把可能会面临的问题描述为一个运输问题或者指派问题或者 它们的变形并进行分析
案例
Case Study
案例研究
案例3：富而克消费用品公司
作业: 第五章奇数习题
西北新闻纸公司（See the Course Package）
▪每一个被指派者只完成一项任务 ▪每一项任务只能由一个被指派者来完成
▪每个被指派者和每项任务的组合有一个相关成本 ▪目标是要确定怎样进行指派才能使得总成本最小
Variants of Assignment Problem 指派问题的变形
指派问题的变形: ▪有一些被指派者并不能进行某一些的任务 ▪任务比被指派者多 ▪被指派者比要完成的任务多 ▪每个被指派者可以同时被指派给多于一个的任务 ▪每一项任务都可以由多个被指派者共同完成
下一讲：网络最优化问题
阅读：Text1,Chapter6 和课件及课程网页相关内容
The End of Session 4
The Assignment Problem 指派问题
现实生活之中，我们也经常遇到指派人员做某项工 作的情况。指派问题的许多应用都用来帮助管理人 员解决如何为一项将要开展进行的工作指派人员的 问题。其他的一些应用如为一项任务指派机器、设 备或者是工厂
Solutions (1)
STATS331,Assignment1,2013SolutionsAugust19,2013Question1a)Here is the Bayes’Box.The rows correspond to the hypotheses S(the email is spam) and¯S(the email is not spam).Hypotheses prior likelihood prior×likelihood posterior S0.50.050.0250.9804¯S0.50.0010.00050.0196 Totals:10.02551b)The top row of the Bayes’Box is equivalent to:P(S|N)=P(S)P(N|S)P(N)(1)orP(S|N)=P(S)P(N|S)P(S)P(N|S)+P(¯S)P(N|¯S)(2)The difference is the expanded version of the marginal likelihood,calculated by using the sum rule(or knowing that it is the sum of prior×likelihood).You could have also given the second row which would be the same but with S and¯S swapped.c)I repeated the Bayes’Box,the only difference being the likelihood P(N|¯S)and the sub-sequent numbers.Note that in this case,the presence of the word Nigeria is evidence that the email is not spam!People often worry about the choice of prior affecting things,but the likelihood can also affect things,and the likelihood is also based on prior information about the meaning of the data.Hypotheses prior likelihood prior×likelihood posterior S0.50.050.0250.3333¯S0.50.10.00050.6667 Totals:10.0751d)The marginal likelihood is the probability of the data,in this case,the probability that an email would say“Nigeria”.This can happen either with S or¯S,and the probability of it occurring via the“spam”route is the same for both people.However,the immigrant hasa higher probability of getting Nigeria in a non-spam email,so the marginal likelihood is higher.In maths,the marginal likelihood comes from the sum rule used with the product rule:P(N)=P(S)P(N|S)+P(¯S)P(N|¯S)(3) and the difference comes in P(N|¯S)which is higher for the immigrant.As everything is positive,the result is higher.Question2a)The three hypotheses are mutually exclusive and exhaustive.Oliver’s innocence is implied if either H2or H3is true,so the prior probability of innocence can be obtained with a simple use of the sum rule:P(innocent)=P(H2or H3)(4)=P(H2)+P(H3)(5)=0.5+0.3(6)=0.8.(7) which is also equal to1−P(H1).b)Similar to above.“Oliver was at the scene”is true if either H1or H2is true.P(at scene)=P(H1or H2)(8)=P(H1)+P(H2)(9)=0.7.(10) c)The Bayes’Box is given below.The three hypotheses are already mutually exclusive and exhaustive so can go right into the Bayes’Box without modification.The prior probabilities were also given in the question.The likelihoods come from the following reasoning:H1:if Oliver is guilty then the probability that the blood would be type“O”is 100%.H2and H3:if Oliver is innocent then the blood is of someone else,the probability it will be type“O”is0.6.Note that the posterior probabilities aren’t that different from the prior probabilities.This information doesn’t help that much in telling which of H1, H2,and H3is correct.Hypotheses prior likelihood prior×likelihood posterior H10.210.20.294H20.50.60.30.441H30.30.60.180.265Totals:10.681d)This is exactly the same as part b)but you use the posterior instead of the prior.P(at scene|D)=P(H1or H2|D)(11)=P(H1|D)+P(H2|D)(12)=0.7353.(13)Note that this is only slightly higher than the prior probability in part b).The data provided very slight evidence that Oliver was at the scene.e)The same Bayes’Box can be constructed but the likelihoods for H2and H3are now different.This is because the probability offinding AB blood given that the suspect is not guilty(i.e.for both H2and H3)is now0.01instead of0.6.Hypotheses prior likelihood prior×likelihood posterior H10.210.20.9615H20.50.010.0050.0240H30.30.010.0030.0144Totals:10.2081Yes,they chose to give a guilty verdict as0.9615≥0.95.Question3This question involves manipulating probability distributions in R.It is most useful for parameter estimation problems involving a single parameter.a)There are several ways.One is u=seq(1,100)and another is u=1:100.You could even do it with a loop,although that wouldn’t be the fastest or most elegant way.b)Here is the code I used.Anything equivalent will do.prior=1/uprior=prior/sum(prior)c)Here is the code I used to make the plot.Anything equivalent will do.plot(u,prior,xlab=’u’,ylab=’Prior Probability’)and here is myplot:prior_mean=sum(u*prior)prior_sd=sqrt(sum(u^2*prior)-prior_mean^2)#These are19.28and24.53e)The probability of u≥10can be found by summing the probabilities in the prior vector,but only including those elements where the value of the u vector is greater thanor equal to10.There are a couple of ways,here’s my favourite.prob1=sum(prior[u>=10])#Sum the subset of the prior vector where u>=10 prob2=sum(prior[u>=50])#Sum the subset of the prior vector where u>=50 #These are0.45and0.13Since the u values are1,2,3,...,100,it is also valid to do,for example,sum(prior[10:100]), although this is less general.f)This involves re-making the prior vector to be uniform,and then repeating part e) using the new prior vector.Here’s my code:prior=rep(1,length(u))prior=prior/sum(prior)prob1=sum(prior[u>=10])prob2=sum(prior[u>=50])#These are0.91and0.51Question4a)The pasted output should look like this.Loading required package:codaLoading required package:latticeLinked to JAGS3.3.0Loaded modules:basemod,bugsCompiling model graphResolving undeclared variablesAllocating nodesGraph Size:5Initializing model|**************************************************|100%|**************************************************|100%b)The code is plot(results$theta,type=’l’)and the plot looks like this:c)The code is hist(results$theta,breaks=100)and the plot looks like this:c)This is easily calculated using mean(results$theta).JAGS doesn’t respect set.seed, which I didn’t realise.The resulting value should be somewhere close to3/7.d)The changed line should look like:draw=jags.samples(m,1000000,thin=1,s=c(’theta’))and the new histogram should look much smoother,very similar to the analytical posterior from the notes(except this is a histogram of samples,not evaluations of the density function):e)I got0.428541using mean(results$theta).The markers were instructed to use a tolerance from0.427to0.43.。
遇到麻烦五条解决麻烦的办法英语作文
遇到麻烦五条解决麻烦的办法英语作文全文共6篇示例，供读者参考篇1Five Ways to Solve ProblemsHi there! My name is Jamie and I'm in the 5th grade. Today I want to talk to you about solving problems. Problems are a part of life, but they don't have to be super hard or scary. I've learned some good ways to deal with problems from my parents, teachers, and even from my own experiences. Let me share five of my favorite ways to solve problems!Talk it outThe first thing I like to do when I have a problem is talk about it with someone I trust. That could be my mom, dad, a teacher, or one of my good friends. Getting advice and a fresh perspective from someone else can be really helpful. They might see something I'm missing or have a good idea I haven't thought of.Talking through the problem step-by-step also helps me better understand what's really going on. Sometimes I realize theproblem isn't as bad as I first thought once I explain all the details out loud. Other times the opposite happens and I realize the problem is more complicated than I knew. But either way, talking makes the problem feel less overwhelming and more manageable.My parents are great at listening without judging and offering guidance when I need it. My friends understand what it's like to be a kid dealing with kid problems too. Having someone's listening ear and getting to vent a little usually makes me feel a lot better already.Make a planOnce I've talked through the problem, the next step is to make a plan for how to solve it. My teacher taught us about breaking big problems down into smaller, more manageable steps. She says having a clear plan helps reduce feeling stressed or overwhelmed.Let's say the problem is that I have a huge homework assignment due next week that I'm worried about finishing in time. I could make a plan that looks something like this:Make a list of all the things I need to do for the assignmentEstimate how long each part will takeSchedule times in my calendar to work on it over the next weekAsk my parents or teacher for help if I get stuck on anythingHaving the steps written down gives me a roadmap to follow. It makes a scary, huge assignment feel much more doable when it's been turned into a series of small, concrete actions to take.Try different solutionsMy dad always reminds me that for any problem, there are usually multiple possible solutions. He says it's smart to think through a few different ways I could approach solving the problem. That way if one solution doesn't work, I can try a different one instead of giving up.Let's go back to that big homework example. One way to complete it could be working on it a little bit each night after school and on the weekend. But another solution could be to ask for an extension, then do it all in one Saturday morning work session. Or maybe I could see if a friend wanted to work on it together and we could help each other.By considering multiple solutions upfront, I give myself options and am more likely to find one that really works for meand my learning style. If procrastinating until the last minute just stresses me out more, then I can cross that solution off the list.Take a breakThis one might sound a little strange, but sometimes the best thing to do when faced with a tricky problem is to take a break from working on it! My brain gets tired easily, and when I'm frustrated it's hard for me to think clearly or be creative in finding solutions.If I've been struggling with a problem for a while with no luck, my mom will suggest I go outside and play for a bit. Or read a book, play video games, do an art project - anything to give my mind a rest. Then when I come back to the problem later with fresh eyes, innovative ideas and solutions have sometimes magically appeared!Getting physical activity and giving my brain a break from concentrating so hard helps me feel refreshed. I almost always end up being able to look at the problem from a new angle after taking a step back for a little while.Ask for helpThe last strategy I'll share is being willing to ask for help when you really need it. Sometimes problems are just too big orcomplicated for one person to solve on their own, especially a kid like me. That's totally okay! The smart thing is to recognize when extra assistance is required.Maybe it's a super challenging math concept I'm having trouble understanding no matter how many times my parents explain it. In that case, asking my teacher for extra help or a tutor could be the solution I need.Or let's say I'm being bullied by someone at school and none of my attempts to resolve it nicely are working. That would definitely be a situation where getting a counselor, principal, or other authority figure involved is the right call.The point is, there's no shame in asking for help! It shows maturity and wisdom to know when a problem is beyond your current capabilities to solve independently. The extra support could make all the difference in finding a good resolution.So those are five of my go-to strategies when I encounter problems, big or small - talk it out, make a plan, try different solutions, take a break, and ask for help when needed. Problems might be inevitable, but they don't have to be permanent or impossible to overcome. With some simple tactics like these, kids can become great problem-solvers!I'm still learning and practicing, but I've already seen how effective these five techniques can be. They've helped me work through problems at school, at home, with friends, you name it. I know they'll continue to serve me well as I get older and the problems get even trickier.What about you? How do you like to solve problems? Maybe you use some of these same strategies, or maybe you have your own unique techniques to share. I'd love to hear them! No matter what, just remember that problems are manageable and you've got this. Thanks for reading, and happy problem-solving!篇2Five Ways to Solve ProblemsHi friends! My name is Tommy and I'm in the 5th grade. Today I want to talk to you about solving problems. We all have problems sometimes, whether it's troubles with friends, family issues, or things not going our way. But don't worry, I have five great tips that can help you solve any problem!Tip #1: Stay CalmThe first thing to do when you have a problem is to stay calm.I know it can be really hard, especially if you're feeling angry,frustrated or upset. But losing your cool never helps solve anything. It just makes the situation worse.Instead, take some deep breaths and count to ten slowly. My mom taught me this trick and it really works! Breathing deeply gets more oxygen to your brain so you can think more clearly. Once you've calmed down, you'll be able to look at the problem in a better way.Tip #2: Think PositiveHaving a positive mindset is so important when you're facing a problem. If you think negatively like "This is too hard, I'll never figure it out," then you're already setting yourself up for failure. But if you think positively like "I can do this if I try my best," you're giving yourself a much better chance of success.Positive thoughts give you confidence and motivation to keep going until you solve the problem. It's like the Little Engine that Could saying "I think I can, I think I can" as it went up the big hill. With a positive attitude, even the biggest problems don't seem so big and tough.Tip #3: Make a PlanOnce you've calmed down and gotten into a positive mindset, it's time to make a plan to solve your problem. Justcharging in without a plan is a bad idea. It's like trying to bake a cake without a recipe - you'll just make a huge mess!For your plan, you need to identify exactly what the problem is. Then you can list out all the possible solutions and decide on the best one to try first. Maybe you need to gather some supplies or materials. Or maybe you need to ask others for help or advice. Getting organized with a good plan is half the battle.Tip #4: Take ActionAfter all your planning and preparing, it's finally time to take action and solve that problem! Don't keep putting it off or you'll never get it done. You have to be brave and dive right in. Yes, it can be a little scary, but remember to stay positive like we talked about.If your first solution doesn't work, don't get discouraged. Just go back to your plan and try the next solution on your list. You may need to get creative and think outside the box. The key is to keep trying and not give up. Winners never quit!Tip #5: Learn From ItWhether you solve your problem or not, it's so important to learn from the experience. Think about what went well and whatdidn't. What could you have done differently or better? There's no such thing as failure, just lessons to learn.The more problems you solve, the better you'll get at it. You'll know what strategies and solutions work best for you. Pretty soon, solving problems will become easy and automatic for you. How cool is that?So there you have it - my five tips for solving any problem that comes your way. Just remember to stay calm, think positive, make a plan, take action, and learn from it all. If you follow these steps, I'm certain you'll become a super problem-solver!I hope you found this essay helpful. Solving problems is a very important life skill that will serve you well as you get older. If you ever get stuck, feel free to ask me for more advice. I'm always happy to help a friend in need. Thanks for reading, and happy problem-solving!篇3Five Ways to Solve ProblemsHey there! Have you ever felt stuck when facing a tough problem or challenge? Maybe your little brother took your favorite toy and you don't know how to get it back. Or perhapsyou're having trouble with a hard math problem for homework. Don't worry, we all run into problems sometimes – that's just part of life! But you know what? There are some pretty cool ways to solve problems and get yourself out of those sticky situations.First up, take a deep breath and stay calm. I know, I know, it's easier said than done when you're feeling frustrated or upset. But getting all worked up and throwing a fit usually doesn't help. It's much better to take a few slow, deep breaths to clear your mind. Once you've calmed down a bit, you can start thinking about the problem in a smarter way.Next, talk it through with someone you trust. Maybe it's your parents, a teacher, or one of your good friends. Describing the problem out loud can often help you see it from a new point of view. And the other person might have some brilliant ideas you haven't thought of yet! They could suggest a solution, or at least give you some advice to help point you in the right direction.Another really useful trick is to take a step back and think about the problem in a different way. Let's say you're arguing with your sibling over a video game and you both want the last turn. Instead of fighting more, you could suggest taking turns or even finding a new game to play together. Looking at the problem from a new angle makes it a lot easier to solve.If you've tried those ideas and you're still stuck, why not take a break for a little while? Step away from the problem and go do something fun - play outside, read a book, or spend some time on your favorite hobby. Giving your brain a rest can help you relax and return to the problem feeling refreshed with a clear mind. You might even discover the perfect solution when you're not thinking about it!Finally, if you've given it your best shot and the problem still won't budge, don't be afraid to ask for more help. Talk to your parents, teacher, coach, or another trusted adult. Explain what you've already tried and ask if they have any other suggestions. Two heads are better than one when it comes to solving tricky problems!Those are five top strategies I've learned for dealing with problems and challenges. Take a breath, talk it through, look at it a new way, take a break, or ask for help - those are all great options. Remember, every problem has a solution if you stay positive and keep working at it. You've totally got this! What was that problem you were stuck on again? With these tips in your back pocket, I bet you can knock it out of the park.篇4Title: Five Ways to Solve ProblemsHi friends! Today I want to talk about problems. We all face problems in our lives, big or small. Maybe you had a fight with your best friend. Maybe you failed a test. Or maybe you lost your favorite toy. Problems can make us feel sad, angry, or worried. But did you know that there are ways to solve problems? Yes, that's right! I'm going to share with you five great ways to solve problems. Are you ready? Let's go!Way #1: Take a Deep BreathWhen you first face a problem, you might feel like everything is falling apart. Your heart might start beating really fast, and you might feel like crying or screaming. That's okay! Those are normal feelings. But here's what you can do: take a deep breath. Breathe in through your nose and out through your mouth. Do this a few times until you feel a little calmer. Taking deep breaths can help you relax and think more clearly about the problem.Way #2: Talk to SomeoneSometimes, when we have a problem, it can help to talk to someone about it. You could talk to your parents, your teacher, or a friend. Telling someone else about your problem can help you see it from a different point of view. They might even havesome good ideas for how to solve it! Plus, it always feels better to share your feelings with someone you trust.Way #3: Make a PlanOnce you've calmed down and talked to someone about your problem, it's time to make a plan. A plan is like a map that shows you how to get from where you are now to where you want to be. For example, if your problem is that you failed a math test, your plan could be: 1) Ask your teacher for extra help, 2) Study for 30 minutes every day after school, and 3) Take the test again in two weeks.Way #4: Try Your BestAfter you've made your plan, it's time to put it into action. This is where you need to try your very best. If your plan involves studying harder, then study as hard as you can. If your plan involves apologizing to your friend, then apologize from your heart. Trying your best is the only way to make your plan work.Way #5: Don't Give UpSometimes, even when we try our best, our plan might not work out the way we wanted it to. That's okay! The most important thing is not to give up. If your first plan doesn't work, make a new plan and try again. Or maybe you need to ask formore help. The point is, keep trying until you find a way to solve your problem.See, solving problems isn't as hard as it seems! All you need to do is take a deep breath, talk to someone, make a plan, try your best, and never give up. Remember, every problem has a solution, and you are smart enough to find it.I hope these five ways to solve problems will help you the next time you face a challenge. Just believe in yourself, and you can overcome any problem that comes your way. Good luck, my friends!篇5Five Ways to Solve ProblemsHi friends! Today I want to talk about problems. Problems are like big rocks in our path that we have to get around or climb over. But don't worry, I have five great tips to help you solve any problem that comes your way!Tip #1: Don't Panic!When you first see a problem, it can feel really scary and make your heart start beating fast. You might even feel like crying. That's okay, feeling worried or upset is normal whenproblems pop up. But you don't want to stay in panic mode for too long. Why? Because when we panic, it's hard to think clearly and come up with good solutions. So give yourself a few minutes to feel anxious, take some deep breaths, and then get ready to face the problem head-on like the brave problem solver you are!Tip #2: Ask For HelpSolving problems can be really hard, especially the really big ones. That's why you shouldn't try to muscle through them all alone. It's super important to ask others for help when you need it. Who can you ask? Your parents, teachers, siblings, friends, coaches, or any other trusted adults in your life. Two (or three or four!) heads are better than one when it comes to cracking tough problems. The people who care about you will be happy you asked for their advice and suggestions instead of suffering in silence.Tip #3: Make a PlanOnce you understand what the problem is, it's time to make a plan to solve it! Think through all the different ways you could handle the situation and what might happen with each option. Which one seems like the smartest or safest choice? Get out a piece of paper and write down each step of your plan. Having itwritten out will make it so much easier to follow. And remember, if your first plan doesn't work, you can always make a new one!Tip #4: Stay PositiveI know, I know, it's really hard to stay positive when you're having a problem. Problems can make us feel sad, frustrated, and want to give up. But getting negative doesn't help solve anything. In fact, it can make problems seem even bigger and more impossible than they really are. Whenever you feel yourself starting to get discouraged, reset your mind. Remind yourself that you ARE a problem solver, you CAN get through this, and a solution could be just around the corner. Maybe take a break, pet a dog, or eat a snack to cheer yourself up. Then go back to your plan with a positive attitude.Tip #5: Don't Give Up!Solving problems is hard work, no doubt about it. You're going to feel like quitting sometimes. But you can't give up! Even if your first few ideas don't work, keep trying. Ask for more help, make a new plan, and keep pushing forward. The greatest inventors, scientists, and leaders never gave up when they had problems. Thomas Edison tried thousands of versions before getting the light bulb right. Abraham Lincoln failed at several jobs and ran for office multiple times before becoming president.If they had quit, we may have missed out on their amazing accomplishments. So don't give up on your problems either! A solution is out there, you just have to stick with it.Those are my five tips for tackling any problems that come your way. I know that if you don't panic, ask for help, make a plan, stay positive, and never give up, you'll be a super problem solver! Isn't it exciting to think about all the challenges you'll overcome? Remember, every problem you face is a chance to practice these skills and get even better. Pretty soon, problems won't seem so rocky or scary anymore. You'll be able to look at them and say, "I'm ready! Bring it on!" Then you can scramble right over them with ease.So what are you waiting for? The next time you run into a problem, put my five tips into action. You've got this!篇6Five Ways to Solve ProblemsHi friends! Have you ever felt stuck when you had a problem? Maybe you were trying to beat a tough video game level or figure out a really hard math question. Problems can be super frustrating, but don't give up! I've learned some tricks that canhelp you solve all kinds of problems. Let me share five of my favorite ways to work through problems.Take a Break and Do Something ElseSometimes when I'm really stuck on a problem, I start to feel overwhelmed and like I'll never figure it out. That's when it's best to take a break! Step away from the problem for a little while and let your mind relax. Go play outside, read a book, or just zone out for a bit. When you come back to the problem later with a fresh mind, you might suddenly see the solution! The break gives your brain a chance to reset so you can look at the problem in a new way.Draw a Picture or DiagramFor problems that are hard to visualize in your head, it can be really helpful to draw a picture or diagram. Like if there's a tough word problem in math about runners on a racetrack, I'll draw a simple diagram of the racetrack and runners. Having a picture in front of me makes it so much easier to understand what's going on. I also love drawing diagrams for problems about fractions or geometry shapes. Breaking it down into a picture or diagram lets you clearly see the different parts and how they relate.Talk It Out With SomeoneTwo heads are better than one when it comes to solving problems! If you're really stuck on something, it can be super helpful to talk it through with a friend, parent, teacher, or anyone else who will listen. Sometimes just saying the problem out loud makes you think about it in a new way. And the other person might have an interesting perspective or insight that you hadn't considered. Plus it's nice to have someone there for moral support when you're feeling frustrated!Break It Down Into Smaller StepsThis is one of my favorite tricks for really complicated, multi-step problems. Instead of looking at the whole problem and feeling overwhelmed, break it down into smaller, easier steps. Solve one little part at a time, and then gradually work your way through the whole thing. It's so much less intimidating when you approach it bit by bit! I also find that physically writing out each step helps keep me organized as I go.Look for Resources and Double CheckIf you've tried everything and still can't figure out the problem, it's time to look for some outside help. Check for any resources you can use - maybe a textbook example, aninstructional video, or even just asking your teacher for some guidance. Double check that you really understand all the facts and aren't missing any key information too. Sometimes going back to square one and making sure you grasp the basics is what you need to finally crack that problem!So those are five of my go-to strategies when I get stuck on a problem. Remember, having trouble with a problem just means your brain is working hard and learning something new. Don't get frustrated! Stay positive, use strategies like taking breaks or drawing diagrams, and you'll get through it. Solving problems might not be easy, but it sure feels awesome when you finally figure it out. Keep practicing and you'll become aproblem-solving master!。
HW2Solution
Homework Assignment 2InstructionsThis assignment is due to be turned in at the start of class on Wednesday February 11. You can work on this assignment by yourself or in a team of two. If you choose to work in a team of two, you should turn in only one assignment per team (with both member’s student IDs on the assignment).The assignment consists of two parts. Part A contains discussion questions. These are NOT to be turned in, they are intended to solidify your understanding of the theoretical concepts that we have discussed. I suggest writing down your answers and comparing them with the solutions that I will upload once the assignments have been turned in. Part B contains assignment problems that must be turned in. Remember that these assignments are graded on a √- ,√, √+ system as detailed in the syllabus. You are free to turn in printouts or a clear, legible, handwritten assignment.Part A: Discussion questions (not to be turned in).1.Explain carefully why liquidity preference theory is consistent with the observation thatthe term structure of interest rates tends to be upward sloping more often than it is downward sloping.If long-term rates were simply a reflection of expected future short-term rates, we would expect the term structure to be downward sloping as often as it is upward sloping. (This is based on the assumption that half of the time investors expect rates to increase and half of the time investors expect rates to decrease). Liquidity preference theory argues that long term rates are high relative to expected future short-term rates. This means that the term structure should be upward sloping more often than it is downward sloping.2.What is meant by (a) an investment asset and (b) a consumption asset? Why is thedistinction between investment and consumption assets important in the determination of forward and futures prices?An investment asset is an asset held for investment by a significant number of people or companies. A consumption asset is an asset that is nearly always held to be consumed(either directly or in some sort of manufacturing process). The forward/futures price can be determined from the spot price for an investment asset. In the case of a consumptionasset all that can be determined is an upper bound for the forward/futures price.3.What is the cost of carry for (a) a non-dividend-paying stock, (b) a stock index, (c) acommodity with storage costs, and (d) a foreign currency?a)the risk-free rate, b) the excess of the risk-free rate over the dividend yield c) therisk-free rate plus the storage cost, d) the excess of the domestic risk-free rate over theforeign risk-freerate.4. Do we expect the futures price of a stock index to be greater than or less than the expected future value of the index? Explain your answer.The futures price of a stock index is always less than the expected future value of the index. This follows from Section 5.14 and the fact that the index has positive systematic risk. For an alternative argument, let μ be the expected return required by investors on the index so that ()0()q T T E S S e -=μ. Because r >μ and ()00r q T F S e -=, it follows that 0()T E S F >.Part B: Homework problems (to be turned in)1. The cash prices of six-month and one-year Treasury bills are 94.0 and 89.0. A 1.5-year bond that will pay coupons of $4 every six months currently sells for $94.84. A two-year bond that will pay coupons of $5 every six months currently sells for $97.12. Calculate the six-month, one-year, 1.5-year, and two-year zero rates.The 6-month Treasury bill provides a return of 6946383%/=. in six months. This is 2638312766%⨯.=. per annum with semiannual compounding or2ln(106383)1238%.=. per annum with continuous compounding. The 12-month rate is 118912360%/=. with annual compounding or ln(11236)1165%.=. with continuous compounding. For the 112year bond we must have 012380501165115441049484R e e e -.⨯.-.⨯-.++=.where R is the 112year zero rate. It follows that 15153763561049484084150115R R e e R -.-..+.+=.=.=.or 11.5%. For the 2-year bond we must have012380501165101151525551059712R e e e e -.⨯.-.⨯-.⨯.-+++=. where R is the 2-year zero rate. It follows that 2079770113R e R -=.=.or 11.3%.2. Problem 4.9. What rate of interest with continuous compounding is equivalent to 15% per annum with monthly compounding?The rate of interest is R where: 12015112R e .⎛⎫=+ ⎪⎝⎭i.e., 01512ln 112R .⎛⎫=+ ⎪⎝⎭01491=.The rate of interest is therefore 14.91% per annum.3. Problem4.12. A three-year bond provides a coupon of 8% semiannually and has a cash price of 104. What is the bond’s yield?Ans: The bond pays $4 in 6, 12, 18, 24, and 30 months, and $104 in 36 months. The bondyield is the value of y that solves05101520253044444104104y y y y y y e e e e e e -.-.-.-.-.-.+++++= Using the Solver or Goal Seek tool in Excel 006407y =. or 6.407%.4. Problem 4.14. Suppose that zero interest rates with continuous compounding are as follows:Calculate forward interest rates for the second, third, fourth, and fifth years.For year4 2,$1*exp(2+f)=exp(2*3)f=6-2 = 4%Year 2: 4.0%Similarly, for year 3, 2*3+f = 3.7*3. Therefore f=5.1%Year 3: 5.1%Year 4: 5.7%Year 5: 5.7%5. A stock is expected to pay a dividend of $1 per share in two months and in five months. The stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. An investor has just taken a short position in a six-month forward contract on the stock.a. What are the forward price and the initial value of the forward contract?b. Three months later, the price of the stock is $48 and the risk-free rate of interest is still 8% per annum. What are the forward price and the value of the short position in the forward contract?a) The present value, I , of the income from the security is given by:0082120085121119540I e e -.⨯/-.⨯/=⨯+⨯=. From equation (5.2) the forward price, 0F , is given by:008050(5019540)5001F e .⨯.=-.=.or $50.01. The initial value of the forward contract is (by design) zero. The fact that the forward price is very close to the spot price should come as no surprise. When the compounding frequency is ignored the dividend yield on the stock equals the risk-free rate of interest.b) In three months:00821209868I e -.⨯/==. The delivery price, K , is 50.01. From equation (5.6) the value of the short forward contract, f , is given by008312(48098685001)201f e -.⨯/=--.-.=.and the forward price is008312(4809868)4796e .⨯/-.=.6. The current price of silver is $30 per ounce. The storage costs are $0.48 per ounce per year payable quarterly in advance. Assuming that interest rates are 10% per annum for all maturities, calculate the futures price of silver for delivery in nine months.The present value of the storage costs for nine months are0.12 + 0.12e −0.10×0.25 + 0.12e −0.10×0.5 = 0.351or $0.351. The futures price is from equation (5.11) given by 0F whereF 0 = (30 + 0.351)e 0.1×0.75= 32.72i.e., it is $32.72 per ounce.7. In early 2012, the spot exchange rate between the Swiss Franc and U.S. dollar was 1.0404 ($ per franc). Interest rates in the U.S. and Switzerland were 0.25% and 0% per annumrespectively, with continuous compounding. The three-month forward exchange rate was1.0300 ($ per franc). What arbitrage strategy was possible? How does youranswer change if the exchange rate is 1.0500 ($ per franc).The true forward price should be:F =Se(r-rf)T= 1.0404 * exp((0.25% -0)*3/12)= 1.04105With the three month forward at 1.03 $ per franc , rather than the 1.04105 $ per franc it should be, I want to convert $s to Francs 3 months forward. Therefore, I borrow 1 franc, convert it spot to get 1.0404 dollars and invest them at the risk free rate. I also buy a 3 month swiss francs forward. My US investment yields:1.0404*exp(0.25%*0.25)=1.04105. I convert that using the forward contract, to yield1.04105/1.03 = 1.01073 francs. I thus make a risk free profit of 0.01073 per francinvested..With three month forward rate as 1.05, my strategy is: Borrow 1 dollar, convert it spot to francs, (I get 1/1.0400 francs) in Switzerland, sell francs forward. Use the forward to convert it back to dollars. At the end of three months, I need to pay out exp(0.25%*0.25) = 1.00063 from my US borrowing. I have 1.0500*1/1.0404 =1.00927. I thereby make a profit of 1.00927-1.00063 =0.00864 for every dollar invested.8.The current spot price of oil is $67.25 per barrel, the 6 month futures price is$69.75/barrel, and the risk-free rate is 4.2% (annualized and continuously compounded).What is the implied storage cost of oil expressed as an annualized continuously compounded rate? Whose storage cost do you think this reflects (Hint: Could you store oil at this rate?)F0 = S0e(r+s)T69.75=67.25e(0.042+s)0.5s = 2* (Ln(69.75/67.25)-0.021)= 3.1%This is the storage cost for the firm with the lowest marginal storage cost in the market. If for example this was not true, and there exists someone with lower marginal storage costs than 3.1% per year,they would execute the strategy of buying spot, and storing and be able to make a risk free arbitrage profit. They would do so until either (1) their marginal storage cost rose, or (2) the forward price fell to reflect their cost.。
请你设计一个创新性的作业写成英语作文
请你设计一个创新性的作业写成英语作文Designing an Innovative AssignmentIn the ever-evolving landscape of education, the need to foster creativity, critical thinking, and practical application of knowledge has become increasingly paramount. As an educator, I firmly believe that the traditional approach to assignments often falls short in igniting the spark of innovation within students. Therefore, I propose the design of an innovative assignment that challenges students to think outside the box and develop solutions that transcend the boundaries of conventional thinking.At the core of this innovative assignment is the concept of problem-based learning. Rather than simply regurgitating information or completing predetermined tasks, students will be presented with a real-world problem or challenge that requires them to engage in active research, analysis, and problem-solving. This approach not only enhances their understanding of the subject matter but also equips them with the essential skills needed to navigate the complexities of the modern world.The assignment will begin with the introduction of a multifaceted problem that encompasses various aspects of the course curriculum. This problem could be drawn from current events, industry trends, or societal issues, ensuring that it resonates with the students and sparks their genuine interest. By presenting a problem that is both relevant and thought-provoking, we can foster a sense of ownership and investment within the students, motivating them to delve deeper into the subject matter.Once the problem is introduced, students will be tasked with conducting extensive research to gather relevant information, identify key stakeholders, and analyze the underlying factors contributing to the problem. This research phase will not only deepen their understanding of the subject matter but also hone their information-gathering and critical-thinking skills. Students will be encouraged to explore a diverse range of sources, including academic literature, industry reports, and real-world case studies, to gain a comprehensive understanding of the problem.With the research phase complete, students will then be required to work collaboratively in teams to develop innovative solutions to the problem. This collaborative approach fosters the development of essential soft skills, such as communication, teamwork, and conflict resolution, all of which are highly valued in the modern workforce.Moreover, the team dynamic encourages the cross-pollination of ideas, leading to the emergence of creative and unconventional solutions that a single student may not have conceived on their own.As the teams work on their solutions, they will be required to present their progress and ideas to the class at regular intervals. These periodic check-ins not only keep the students accountable but also provide opportunities for peer feedback and constructive criticism. By exposing their ideas to the scrutiny of their classmates and the instructor, students will learn to refine their solutions, address potential weaknesses, and incorporate diverse perspectives, further enhancing the quality and originality of their work.The culmination of the assignment will be a final presentation, where each team will showcase their innovative solution to the problem. This presentation will not only demonstrate the students' mastery of the subject matter but also their ability to effectively communicate their ideas and defend their proposed solutions. The presentation will be evaluated not only on the technical merits of the solution but also on the creativity, feasibility, and potential impact of the proposed approach.To further incentivize innovation and creativity, the assignment will incorporate a competitive element. The most innovative and impactful solutions will be recognized and rewarded, providingstudents with the motivation to push the boundaries of their thinking and strive for excellence. This competitive aspect not only fosters a spirit of healthy rivalry but also encourages students to continuously refine and improve their work, ultimately leading to the development of truly groundbreaking solutions.Moreover, the innovative assignment will incorporate opportunities for real-world application and implementation. Students may be encouraged to collaborate with local organizations, businesses, or community groups to pilot their solutions, gaining valuable practical experience and potentially making a tangible difference in the world around them. This hands-on approach not only enhances the students' understanding of the problem but also instills a sense of civic responsibility and social awareness.In conclusion, the design of this innovative assignment aims to transform the traditional educational landscape by fostering creativity, critical thinking, and practical application of knowledge. By presenting students with real-world problems and empowering them to develop innovative solutions, we can cultivate a generation of problem-solvers, innovators, and change-makers who are equipped to tackle the challenges of the 21st century. Through collaborative teamwork, iterative refinement, and opportunities for real-world implementation, this assignment will not only enhance the students'academic performance but also prepare them for the dynamic and ever-evolving demands of the modern workforce and society.。
必写作业和选写作业英语
In an educational context,assignments are typically categorized into two types: mandatory or required and elective or optional.Heres a detailed look at both types of assignments in English:Mandatory Assignments必写作业1.Definition:These are tasks that students must complete as part of their coursework. They are often graded and contribute to the final grade in a class.2.Importance:Mandatory assignments are crucial for students to demonstrate their understanding of the subject matter and to meet the learning objectives set by the course.3.Examples:Essays:Students may be required to write essays on specific topics to develop critical thinking and writing skills.Research Papers:These involve indepth investigation into a subject and are often used in higherlevel courses.Problem Sets:Common in math and science classes,these assignments involve solving problems to apply theoretical knowledge.Lab Reports:In science courses,students may be required to perform experiments and write detailed reports on their findings.4.Consequences of NonCompletion:Failure to complete mandatory assignments can result in a lower grade,academic probation,or even failure of the course.5.Submission:These assignments usually have strict deadlines and are submitted througha specified method,such as a learning management system or in person.Elective Assignments选写作业1.Definition:These are tasks that students can choose to complete for additional credit or to deepen their understanding of the subject.2.Importance:While not required for course completion,elective assignments can enhance a students learning experience and provide opportunities for extra practice or exploration of topics of interest.3.Examples:Extra Credit Projects:These may include presentations,additional essays,or creativeprojects that go beyond the standard coursework.Advanced Reading:Students might choose to read beyond the assigned texts to gain a deeper understanding of the subject.Peer Review:Students can opt to review and provide feedback on their peers work, which can be a valuable learning experience.4.Benefits:Completing elective assignments can lead to a better understanding of the material,improved grades,and a more engaging educational experience.5.Submission:The submission process for elective assignments may be more flexible than for mandatory assignments,and they may not always be graded.6.Incentives:Teachers may offer incentives for completing elective assignments,such as bonus points or the opportunity to choose a topic for a future assignment.Both types of assignments play a significant role in a students educational journey. Mandatory assignments ensure that students meet the minimum requirements of their courses,while elective assignments offer the chance to go above and beyond,enriching the learning experience and potentially boosting academic performance.。
fromproblemstosolutions 教案
fromproblemstosolutions 教案教案：从问题到解决方案课程信息•课程名称：从问题到解决方案•适用年级：中学和高中•学科：创新思维•学时：2小时教学目标•了解问题解决的基本概念和步骤•学会运用创新思维解决问题•提升学生的批判性思维和创新能力教学准备•白板和黑板•彩色粉笔和白色粉笔•学生纸和笔•活动材料：由教师准备问题和相关资料教学过程导入（10分钟）•向学生介绍课程名称和学习目标•引入问题解决的概念，让学生思考日常生活中遇到的问题讨论（15分钟）•将学生分成小组，让每个小组思考一个问题并讨论•指导学生思考问题的原因和可能的解决方案•让每个小组选择一个问题，并简要汇报给全班课堂讲解（15分钟）•介绍问题解决的基本步骤：定义问题、收集信息、生成解决方案、选择最佳方案、实施方案、评估结果•解释每个步骤的重要性和具体操作方法小组活动（30分钟）•让每个小组选择一个问题，并根据问题解决步骤设计解决方案•鼓励学生运用创新思维，提供多样化的解决方案•教师定期巡回指导和帮助学生总结（10分钟）•指导学生总结小组讨论的结果和他们的解决方案•回顾课程学习目标，让学生思考他们在课程中学到了哪些东西•鼓励学生分享他们在课堂中的心得体会评估与作业•作业：要求学生撰写一篇关于他们在小组活动中选择和设计解决方案的报告•评估标准：报告中是否包含问题定义、信息收集、解决方案生成、方案选择、方案实施和评估的内容拓展活动•鼓励学生在日常生活中运用问题解决的基本步骤，解决更多实际问题•组织学生参加创新比赛或项目，提升他们的创新能力和解决问题的能力参考资料•无导入（10分钟）•向学生介绍课程名称和学习目标，强调课程的重要性和实用性。
•提出一个简单问题，如“你遇到过什么问题？”，鼓励学生思考并回答。
讨论（15分钟）•将学生分成小组，每个小组讨论并选择一个问题。
•引导学生思考问题的原因和可能的解决方案，鼓励多样化的思考。
•让每个小组选择一个问题，并简要汇报给全班，分享他们的思考结果。
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Assignment #2 Name___________________________FIN 4310-501Spring 2016BE SURE TO SHOW YOUR WORK1. Baltimore Baking is preparing its cash budget and expects to have sales of $30,000 in January, $35,000 in February, and $35,000 in March. If 20% of sales are for cash, 40% are credit sales paid in the month after the sale, and another 40% are credit sales paid 2 months after the sale, what are the expected cash receipts for March?Payments:Cash 20%Pay 2nd month 40%Pay 3rd month 40%CollectionsSales for Mos. January February March January $30,000 $6,000 $12,000 $12,000 February 35,000 7,000 14,000 March 35,000 _____ ______ 7,000 Total collections for month: $6,000 $19,000 $33,0002. Krackle Korn Inc. had credit sales of $3,500,000 last year and its days sales outstanding was DSO = 35 days. What was its average receivables balance, based on a 365-day year?Sales $3,500,000DSO 35Receivables = (Sales per day)(DSO) = Sales/365 × DSO = $335,6163. Buchholz Corporation follows a moderate current asset investment policy, but it is now considering a change, perhaps to a restricted or maybe to a relaxed policy. The firm's annual sales are $400,000; its fixed assets are $100,000; its target capital structure calls for 50% debt and 50% equity; its EBIT is $35,000; the interest rate on its debt is 10%; and its tax rate is 40%. With a restricted policy, current assets will be 15% of sales, while under a relaxed policy they will be 25% of sales. What is the difference in the projected ROEs between the restricted and relaxed policies?Sales $400,000 Debt ratio 50% Interest rate 10% Fixed assets $100,000 EBIT $35,000 Tax rate 40%15% CA/Sales, relaxed 25%CA/Sales,restrictedRestricted RelaxedCA $ 60,000 $100,000FA 100,000 100,000Total assets $160,000 $200,000Debt $ 80,000 $100,000Equity 80,000 100,000Total liab. & capital $160,000 $200,000EBIT $ 35,000 $ 35,000Interest 8,000 10,000EBT $ 27,000 $ 25,000Taxes 10,800 10,000NI $ 16,200 $ 15,000ROE 20.25% 15.00%Difference in ROE = 5.25%4. Data on Nathan Enterprises for the most recent year are shown below, along with the days sales outstanding of the firms against which it benchmarks. The firm's new CFO believes that the company could reduce its receivables enough to reduce its DSO to the benchmarks' average. If this were done, by how much would receivables decline? Use a 365-day year.Sales $110,000Accounts receivable $16,000Days sales outstanding (DSO) 53.09Benchmark days sales outstanding (DSO) 20.00Original Benchmark ReceivablesatData RelatedDSO DSO BenchmarkLevelSales $110,000Receivables and DSO $16,000 53.09 20.00New receivables = DSO × (Sales/365)=$6,027Reduction in receivables = Originalreceivables − New receivables =$9,973Alternative solution:(Change in DSO/Original DSO) × Orig.receivables =$9,9735. Thornton Universal Sales' cost of goods sold (COGS) average $2,000,000 per month, and it keeps inventory equal to 50% of its monthly COGS on hand at all times. Using a 365-day year, what is its inventory conversion period?Monthly COGS = $2,000,000Inventory/COGS = 50.0%Annual COGS = $24,000,000Avg. inventory = $1,000,000Inv. conv. period = Inv./COGS per day = Inv./(Annual COGS/365) = 15.2 days6. Data on Liu Inc. for the most recent year are shown below, along with the inventory conversion period (ICP) of the firms against which it benchmarks. The firm's new CFO believes that the company could reduce its inventory enough to reduce its ICP to the benchmarks' average. If this were done, by how much would inventories decline? Use a 365-day year.Cost of goods sold = $85,000Inventory = $20,000Inventory conversion period (ICP) = 85.88Benchmark inventory conversion period (ICP) = 38.00Original Benchmark ICP atData RelatedICP ICP BenchmarkLevelCost of goods sold $85,000Inventory and ICP $20,000 85.88 38.00New inventory = ICP × (COGS/365) =$8,849Reduction in inventories = OriginalInv. − New Inv. =$11,151Alternative solution:(Change in ICP/Original ICP) × Orig.Inv. =$11,1517. Data on Mertz Co. for the most recent year are shown below, along with the payables deferral period (PDP) for the firms against which it benchmarks. The firm's new CFO believes that the company could delay payments enough to increase its PDP to the benchmarks' average. If this were done, by how much would payables increase? Use a 365-day year.Cost of goods sold = $75,000Payables = $5,000Payables deferral period (PDP) = 24.33Benchmark payables deferral period = 30.00Original Benchmark PayablesatData RelatedPDP PDP BenchmarkLevelCost of goods sold $75,000Inventory and PDP $5,000 24.33 30.00 New payables = PDP × (COGS/365) = $6,164 Increase in payables = New Payables −Original Payables =$1,164Alternative solution:(Change in PDP/Original PDP) × Orig.Payables =$1,1648. Marshall Inc. recently hired your consulting firm to improve the company's performance. It has been highly profitable but has been experiencing cash shortages due to its high growth rate. As one part of your analysis, you want to determine the firm's cash conversion cycle. Using the following information and a 365-day year, what is the firm's present cash conversion cycle?Average inventory = $75,000Annual sales = $600,000Annual cost of goods sold = $360,000Average accounts receivable = $160,000Average accounts payable = $25,000Avg. inventory = $75,000 Annual sales = $600,000 Avg. receivables = $160,000 Annual COGS = $360,000 Avg. payables = $25,000 Days in year = 365Inv. conv. period = Inv./(COGS/365) 76.0+ DSO = Receivables/(Sales/365) 97.3− Payables deferral =−25.3Payables/(COGS/365)Cash conversion cycle (CCC) 148.0。