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...George Alan O'Dowd at Barnehurst Hospital in Bexley, Kent on 14 June 1961, to Gerald and Dinah O'Dowd, who were originally from Thurles, County Tipperary in Ireland. He is one of six children. His siblings are Richard, Kevin, David, Gerald, and Siobhan. He was a follower of the New Romantic movement which was popular in Britain in the early 1980s. George and his friend Marilyn were regulars at The Blitz, a trendy London nightclub run by Steve Strange of the group Visage. George and Marilyn also worked at the nightclub as cloakroom attendants. Boy George's androgynous style of dressing caught the attention of music executive Malcolm McLaren, who arranged for George to perform with the group Bow Wow Wow, featuring Annabella Lwin. Boy George's tenure with Bow Wow Wow proved quite popular, much to the dismay of Lwin, the group's actual lead singer. His association ended soon afterwards and he started his own group with bassist Mikey Craig. Next came Jon Moss (who had drumming stints with The Damned and Adam and the Ants), and then Roy Hay. The group called themselves In Praise of Lemmings, but the name was later abandoned, and they settled on the name Culture Club The band recorded demos that were paid for by EMI Records but the label declined to sign them. Virgin Records expressed interest in signing the group in the UK, while Epic Records would handle the US distribution. They recorded their debut album Kissing to Be Clever and it was released in 1982. The......
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...This is Pow Wow He stood among the dancers in the grass arena, still and poised, ready to outperform his competition. Finally, the loudspeakers rang out with the beat of the drum, setting the dancers into motion for the last time that year. Slowly, they began to come alive quickening their pace as the singers cried out their song. His steps were perfect, each one placed with meaning, precisely timed with the beat. His feathers bobbed up and down, echoing his movements. Beads of sweat streamed down his painted face and caught at the end of his nose before being thrown onto the moccasin-beaten grass. His bells and headdress shook with each step, the red and yellow colors of his regalia blurring as he spun. His heart raced as the song reached its peak, his hands wet with nervous sweat. He timed his steps, concentrated on the beat, and took a deep breath, preparing for the move that would bring him victory: a complete and perfect handspring. As his feet came down over his body, thousands of Indians around the arena caught their breath. He pretended not to notice, continuing to pound his moccasins into the ground in rhythm with the drum. As the last beat rang, he froze his body in the stance of a warrior, posing as still as he had before the song began. His chest heaved and sweat poured down his broad, smiling face. I joined my family and the crowd in cheering for him, proud to be his niece. Dancers like him and moments like these are what keep our culture alive. This is why I......
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...Additional information, including supplemental material and rights and permission policies, is available at http://ite.pubs.informs.org. Vol. 9, No. 1, September 2008, pp. 1–9 issn 1532-0545 08 0901 0001 informs ® doi 10.1287/ited.1080.0014 © 2008 INFORMS INFORMS Transactions on Education Using Simulation to Model Customer Behavior in the Context of Customer Lifetime Value Estimation Shahid Ansari, Alfred J. Nanni Accounting and Law Division, Babson College, Wellesley, Massachusetts 02457 {sansari@babson.edu, nanni@babson.edu} Dessislava A. Pachamanova, David P. Kopcso Mathematics and Science Division, Babson College, Wellesley, Massachusetts 02457 {dpachamanova@babson.edu, kopcso@babson.edu} T his article illustrates how simulation can be used in the classroom for modeling customer behavior in the context of customer lifetime value estimation. Operations research instructors could use this exercise to introduce multiperiod spreadsheet simulation models in a business setting that is of great importance in practice, and the simulation approach to teaching this subject could be of interest also to marketing and accounting instructors. At Babson College, the spreadsheet simulation exercise is part of an integrated one-case teaching day of the marketing, accounting, and operations research disciplines in the full-time MBA program, but the exercise is directly transferable to stand-alone courses as well. In our experience, students......
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...Jet Copies Breakdown Cumulative Prob Time Between Breakdown Probability Cumulative Probability Repair Time (days) Probability (Uniform) Cumulative Probability Sales Vol. F(x) = .0275x2 x = 20*sqrt(r/11) 0.20 0 1 0.143 0 2000 0.45 0.20 2 0.143 0.143 3000 0.25 0.65 3 0.143 0.286 4000 0.10 0.90 4 0.143 0.429 5000 0.143 0.571 6000 0.143 0.714 7000 0.143 0.857 8000 Breakdowns "Random #, r1 ( rand() )" Time Between Breakdowns, x (weeks) Cumulative Time, x (weeks) Random #, r2 ( rand() ) Repair Time (days) "Random #, r3 ( rand() )" Number of Sales Per Day Revenue Lost Per Day, .10s Revenue Lost 1 0.87461092 5.639506491 5.639506491 0.812564485 3 0.618968125 6000 $600 $1,800 2 0.619910638 4.747863204 10.3873697 0.046586853 1 0.732973872 7000 $700 $700 3 0.648856412 4.857445687 15.24481538 0.149309122 1 0.415056638 4000 $400 $400 4 0.202647621 2.714591016 17.9594064 0.93071048 4 0.041572713 2000 $200 $800 5 0.035360553 1.133948101 19.0933545 0.985291726 4 0.84598125 7000 $700 $2,800 6 0.59729191 4.660440518 23.75379502 0.94815507 4 0.822362216 7000 $700 $2,800 7 0.538230976 4.424029326 28.17782434 0.14855159 1 0.120220407 2000 $200 $200 8 0.187726352 2.612740475 30.79056482 0.883373483 3 0.508932837 5000 $500 $1,500 9 0.661050419 4.902876406 35.69344123 0.069376826 1 0.265850047 3000 $300 $300 10 0.031228616 1.065638801...
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...Exam Stat 1204 ibsu basic THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A company hires management trainees for entry level sales positions. Past experience indicates that only 10% will still be employed at the end of 9 months. Assume the company recently hired 6 trainees. 1) What is the probability that three of the trainees will still be employed at the end of 9 months? A) 0.0415 B) 0.0446 C) 0.0146 D) 0.0012 2) What is the probability that at least two of the trainees will still be employed at the end of 9 months? A) 0.9841 B) 0.0159 C) 0.1143 D) 0.0984 THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A basketball player makes 80 percent of his free throws during the regular season. Consider his next 8 free throws. 3) What is the probability that he will make exactly 6 free throws? A) 0.1468 B) 0.3355 C) 0.2936 4) What the probability that he will make at least 6 free throws? A) 0.2936 B) 0.3355 C) 0.7969 D) 0.1678 D) 0.1468 THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A cereal manufacturer produces a cereal that claims to contain 16 ounces in each box. A sample of boxes results in the following table. 14 15 16 17 Weight in Ounces Probability 0.10 0.30 0.40 0.20 5) What is the mean weight of the sample of cereal boxes? A) 16.0 B) 15.7 C) 15.5 D) 16.5 D) 1.25 6) What is the standard deviation of the weight of cereal in the boxes? A) 1.19 B) 0.90 C) 0.81 THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In an......
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...could result in difficult summarization. A closed-ended question might work better in this instance. Rephrase like: Do you prefer an artificial sweetener? 7. Confusing Words - If a plane crashes on the border of New York and New Jersey, where would you burry the casualties? 8. Double Barreled Question – Would you be in favor of imposing a tax on tobacco to pay for health care related diseases? 6.1 What is the difference between the probability distribution of a discrete random variable and that of a continuous random variable? Explain. A continuous random variable is achieved from information that can be measured instead of counted. A continuous random variable is a variable that can assume an infinite amount of possible values. The probability distribution of a discrete random variable included values that a random variable can assume and the corresponding probabilities of the values. The probability distribution of a continuous random variable has two characteristics: 1. The probability that x assumes a value in any interval lies in the range 0 to 1. 2. The probability of all the (mutually exclusive) intervals within which x can assume a value is 1. A continuous probability distribution differs from a discrete...
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...1 Mathematics for Management Concept Summary Algebra Solving Linear Equations in One Variable Manipulate the equation using Rule 1 so that all the terms involving the variable (call it x) are on one side of the equation and all constants are on the other side. Then use Rule 2 to solve for x. Rule 1: Adding the same quantity to both sides of an equation does not change the set of solutions to that equation. Rule 2: Multiplying or dividing both sides of an equation by the same nonzero number does not change the set of solutions to that equation. Straight Lines: Slope Intercept Form A straight line with slope m and y-intercept (b, 0) has the equation y = mx + b. Point Slope Form of a Line Equation Given two points on a line, (x0, y0) and (x1, y1), find the line's slope m =1−01−0. Then the equation of the line may be written as y – y0 = m(x – x0). Solving Two Linear Equations Two linear equations in two variables (call them x and y) have no solution, an infinite number of solutions, or a unique solution. You may solve two linear equations by either substitution or elimination. Substitution: Use one equation to solve for one variable in terms of the other (say, x in terms of y). Then substitute this relationship for each occurrence of x in the remaining equation. Now solve the remaining equation for y. Given that you know x in terms of y, you also know x. Elimination: Add a multiple of one equation to the other equation to eliminate a variable (say, x) from the......
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...all the possibilities through sampling and probability. While it would be more accuracy to follow the physical process to make the decision based on true, random occurrences, JET Copies wants to know the number of breakdowns and repair time for a year which calls for this simulation of random numbers. To begin this simulation the repair time table had to be computed because it would give an introduction overview of the probability of the repair time needed to fix any breakdowns; it would also be needed to fulfill some details in the next table as well. Based on this table the following information was gathered: the probability that it would take one to two days to repair a breakdown would be 65 percent whereas for it to take three days or more would be 90 percent. After this table was created it was time to focus on the main table of the simulation which would provide more detailed information from a probability basis. The first column of the second table was to list the number of breakdowns that might occur within a year, and for this table I stopped at 13 breakdowns per year and this will be explained later in this paper. Next, because this simulation is using random numbers, random numbers had to be created, also known as pseudorandom numbers, generated by the computer following the formula =RAND(). After the random numbers had been...
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...Assignment 1 1. Prove that : P (E ∪ F ∪ G) = P (E) + P (F ) + P (G) − P (E c ∩ F ∩ G) − P (E ∩ F c ∩ G) − P (E ∩ F ∩ Gc ) − 2P (E ∩ F ∩ G). 2. Prove the followings: (a) (∪∞ An )c = ∩∞ Ac . (cf) In order to prove A = B for two sets A and B, you i=1 n n=1 should show that ∀x ∈ A, x ∈ B, and vice versa.) (b) Let F be a σ-field on Ω. If An ∈ F for all n ∈ N, then ∩∞ An ∈ F. n=1 3. An elementary school is offering 3 language classes: one in Chinese, one in Japanese, and one in English. These are open to any of the 100 students in the school. There are 28 students in the Chinese class, 26 in the Japanese class, and 16 in the English class. There are 12 students that are in both Chinese and Japanese, 4 that are in both Chinese and English, and 6 that are in both Japanese and English. In addition, there are 2 students taking all 3 classes. (a) If a student is chosen randomly, what is the probability that he or she is not in any of these classes? (b) If a student is chosen randomly, what is the probability that he or she is taking exactly one language class? (c) If 2 students are chosen randomly without replacement, what is the probability that at least one is taking a language class? 4. A CEO wants to decide how much to invest on a project. If the firm invest x, then the probability of success is 1 − e−2x . If the project succeeds, then the firm earns 1, and if not, nothing. Let Y be the earning from the project. The profit function of the firm is given by π(Y |x) = Y − x. (a) Derive......
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...46 Probability, Random Variables and Expectations Exercises Exercise 1.1. Prove that E [a + b X ] = a + b E [X ] when X is a continuous random variable. Exercise 1.2. Prove that V [a + b X ] = b 2 V [X ] when X is a continuous random variable. Exercise 1.3. Prove that Cov [a + b X , c + d Y ] = b d Cov [X , Y ] when X and Y are a continuous random variables. Exercise 1.4. Prove that V [a + b X + c Y ] = b 2 V [X ] + c 2 V [Y ] + 2b c Cov [X , Y ] when X and Y are a continuous random variables. ¯ Exercise 1.5. Suppose {X i } is an sequence of random variables. Show that V X = V 2 2 σ where σ is V [X 1 ]. time. 1.4 Expectations and Moments 47 i. Assuming 99% of trades are legitimate, what is the probability that a detected trade is rogue? Explain the intuition behind this result. ii. Is this a useful test? Why or why not? Exercise 1.13. You corporate finance professor uses a few jokes to add levity to his lectures. He is also very busy, and so forgets week to week which jokes were used. i. Assuming he has 12 jokes, what is the probability of 1 repeat across 2 consecutive weeks? ii. What is the probability of hearing 2 of the same jokes in consecutive weeks? iii. What is the probability that all 3 jokes are the same? iv. Assuming the term is 8 weeks long, and they your professor has 96 jokes, what is the probability that there is no repetition across the term? Note: he remembers the jokes he gives in a particular lecture, only forgets across...
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...requirements- model for categorical variables • Total number of observations, n, is fixed • The outcomes of all observations are independent • Each observation falls into just one of 2 categories • All observations have the same probability of success It is okay to ignore dependence if the trials make up less than 10% of the population P hat is a statistic – p(hat)= X/n Bernoulli Distribution- simulates one sample and see the individual successes and failures Binominal Distribution- simulates several samples and see the number of successes and failures in each sample Sampling error- the difference between sample proportions and the true proportion. This is the sample variability from one sample to the next. Data AVERAGE STDEV.S Discrete random variables X1p1+ xnpn Sqrt(var) Bern Sum P Sqrt(pq) Binomial, X is # successes in n trials Sum N*p Sqrt(np*q) Sample proportion p(hat)=X/n Sum P(hat) Sqrt(pq/n) Sample mean...
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...(week 2) 1 Bernoulli, Binomial, Poisson and normal distributions. In this excercise we deal with Bernoulli, binomial, Poisson and normal random variables (RVs). A Bernoulli RV X models experiments, such as a coin toss, where success happens with probability p and failure with probability 1 − p. Success is indicated by X = 1 and failure by X = 0. Therefore, the probability mass function (pmf) of X is P {X = 0} = 1 − p, P {X = 1} = p (1) A binomial random variable (RV) with parameters (n, p) counts the number of successes in n independent Bernoulli trials that succeed with probability p. Thus, we can write a Binomial RV Y as n Y = i=1 Xi (2) where the Xi are Bernoulli RVs with pmfs as in (1). The pmf of a binomial RV is easily derived by noting that we have X = x for some integer x between 0 and 1 if and only there are x successful Bernoulli trials – something that happens with probability px – and n − x failed experiments – which happens with probability (1 − p)n−x – and that there are n different ways in which this could happen. x Thus n x n! px (1 − p)n−x , x = 0, 1, . . . , n. (3) p(x) := P {X = x} = p (1 − p)n−x = (n − x)!x! x A Poisson RV X takes values in the nonnegative integers. We say that X is Poisson with parameter λ it its pmf is λx p(x) = e−λ , x = 0, 1, . . . (4) x! Different from the other two, a normal random variable X can take any real value (not just 0 or 1 like the Bernoulli or integers between 0 and n for the binomial or nonnegative......
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...Case Study: Warren Agency Inc. I. Introduction The Warren Case Study is about the analysis of the problem of Mr. Thaddeus Warren on whether to accept or reject the offer to sell of a prospective client. The client approached him with an offer to sell three properties under certain strict conditions. In making the analysis for this case, a diagram was made, the cumulative profit for each possible outcomes were estimated, and the expected value analysis based on the selling probability estimated by Warren was also computed. All other factors involved that may affect the outcome of a sale is not considered. Only the condition set forth by the client as well as the estimated selling costs and selling probabilities were considered. This analysis, while in the third person is from the point of view of Mr. Warren, the owner of Warren Agency, Inc. II. Statement of the Problem The major problem of the case is whether Warren would accept or reject the proposition of the client. If Warren would accept the proposition of the client, Warren would have to decide on the following: 1. If he will be successful in selling A, would he continue in selling B or C or stop selling any of the properties; 2. If he will continue selling B or C after successfully selling A, which will he sell next, B or C? 3. If he will be successful in selling B, will he continue to sell C or stop selling? 4. If he chose C and succeeded selling it, will he continue to sell B or stop selling? ...
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...James W. Taylor February 2012 Imperial College EMBA 2012 Quantitative Methods Individual Assignment This assignment consists of two parts. Part A is worth 50% of the marks, and Part B is worth the remaining 50%. Your report for the two parts should consist of no more than 1,500 words. Part A – Blanket Systems Blanket Systems is developing and testing a new computer workstation, OB1, which it will introduce to the market in the next 6 months. OB1 will be sold under a three-year warranty covering parts and labour. The company has decided to subcontract the service support for the warranty and has entered negotiations about the support contract with Fixit Inc. Fixit has proposed two different pricing schemes for the subcontract. The first involves the payment of a fixed fee of $1,000,000 and the second a variable fee of $250 per workstation sold, subject to a minimum fee of $350,000. Under both schemes, the payment will be made one year after the introduction of the workstation to the market at which point the product will be replaced by newer models not covered by the warranty service subcontract. At the moment, there is uncertainty about the sales potential of the new workstation. Sales of OB1 are expected to come from two sources: (i) the successful closure by senior management of a major purchase of 2000 units by a long standing customer, (ii) the efforts of regional sales offices. Given the state of the negotiations with the long-standing customer, the current estimate......
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...Jamie Banks, Ernie Moore and Terri Jones were students in State University. They always have to go far to make copies in Klecko’s copy center as there was no copying service nearby where they live by the south gate. One day while James was standing in line at Klecko’s copy center waiting for his turn, he realizes how much time they are wasting just by waiting as most students use the same machine to get copies. James got an idea from other student who was waiting for his turn as James, if he can have a copy center by the Southgate where most of the students live, he easily can make lots of money. James shares his idea with friends Ernie and Terri and they liked the idea. Three of them decided to start the copying business and they would call it JET Copies named after the first letter of their name. They bought a copier similar to the one used at the university for $18,000.00.They enquire about the reliability of the copier and came to know that the university copier broke down frequently and when it did it often require between 1 and 4 days to get it repaired. As Repair time include the time portion during which technicians are working on a machine to effect repair starting from preparation, fault location, fault correction and final check time, it needs time between 1 and 4 days to get it repaired. During this repair time they will always lose Revenue and they become worried. So they decided they might need back up copier to use in these repair time in......
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