.................................................................................... 3 Part I .......................................................................................................................................................... 3 1) Estimation of the Source Power ................................................................................................... 4 2) Quantization Error and SQNR Values............................................................................................ 4 3) Non-uniform Pulse Code Modulation and the use of -law companders .................................... 7 4) N=128 and N=256 Quantization Levels ......................................................................................... 8 Part 2)...................................................................................................................................................... 14 1) The Analysis of the Source Power, SQNR and Quantization Error for Speech Signal ................. 14 2) Non-uniform Quantization of the Speech Signal with µ-Law Compander ................................. 18 Part...
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...Case Study#2 The XYZ Company Katharine Rally is the vice president of operations for the XYZ Company. She oversees operations at a plant that manufactures components for hydraulic systems. Katharine is concerned about the plant’s present production capability. She has reduced the decision situation to three alternatives. The first alternative, which is fully automation, would result in significant changes in present operations. The second alternative, which is semi-automation, involves fewer changes in present operations. The third alternative is to make no changes (do nothing). As a manager of the plant management team, you have been assigned the task of analyzing the alternatives and recommending a course of action. The capital investment and annual revenue for the first two alternatives are shown in the following table: |Alternative |Capital Investment |Future Sales |Annual Revenue | |A |$300,000 |Good |$250,000 | | | |Average |$100,000 | | | |Poor |$50,000 | |B |$85,000 |Good |$100,000 | | | ...
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...Chapter 9 Random Numbers This chapter describes algorithms for the generation of pseudorandom numbers with both uniform and normal distributions. 9.1 Pseudorandom Numbers 0.814723686393179 Here is an interesting number: This is the first number produced by the Matlab random number generator with its default settings. Start up a fresh Matlab, set format long, type rand, and it’s the number you get. If all Matlab users, all around the world, all on different computers, keep getting this same number, is it really “random”? No, it isn’t. Computers are (in principle) deterministic machines and should not exhibit random behavior. If your computer doesn’t access some external device, like a gamma ray counter or a clock, then it must really be computing pseudorandom numbers. Our favorite definition was given in 1951 by Berkeley professor D. H. Lehmer, a pioneer in computing and, especially, computational number theory: A random sequence is a vague notion . . . in which each term is unpredictable to the uninitiated and whose digits pass a certain number of tests traditional with statisticians . . . 9.2 Uniform Distribution Lehmer also invented the multiplicative congruential algorithm, which is the basis for many of the random number generators in use today. Lehmer’s generators involve three integer parameters, a, c, and m, and an initial value, x0 , called the seed. A September 16, 2013 1 2 sequence of integers is defined by xk+1 = axk + c mod m. Chapter 9. Random Numbers The...
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...layer, and the primary recovery rate (in barrels per acre per foot of thickness). Based on geological information, the following probability distributions have been estimated –Estimate of Productive Area Acres Probability 8,000 - 9,000 0.05 9,000 - 10,000 0.10 10,000 - 11,000 0.15 11,000 - 12,000 0.35 12,000 - 13,000 0.25 13,000 - 14,000 0.10 –Estimate of Pay Thickness Smallest Value: 15 ft.. Most Likely Value: 50 ft.. Largest Value: 120 ft.. –Estimate of Primary Recovery Uniform Distribution: Minimum Value: 20 bbl./acre-ft.. Maximum Value: 90 bbl./acre-ft.. Using @Risk Open @Risk (it is available under Start->Programs->Palisade Decision Tools->@Risk 4.5 for Excel). Excel should come up with 2 additional toolbars. For this problem we will need the following distributions: Productive area: discrete distribution, described by a histogram, represented by RISKHISTOGRM(8000, 14000, {0.05, 0.10, 0.15, 0.35, 0.25, 0.10}) Pay thickness: triangular distribution, with a minimum value of 15ft, maximum value of 120ft, and most likely value of 50ft, represented in @Risk by RISKTRIANG(15, 50, 120) Primary Recovery Rate: uniform distribution, with any value being equally likely in the interval 20-90 bbl./acre-ft, represented by RISKUNIFORM(20,90). @Risk offers the above functions, together...
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...Chunlu Xiao STAT 2501 Project Benford’s and Zipf’s Law Abstract Both Benford’s and Zipf’s Law are the result from a lot of real life data, and they are relative and can be applied in our real life. This paper will introduce and explain these two laws in a simply way. Benford’s Law Benford's Law, also called the First-Digit Law, refers to the frequency distribution of digits in many (but not all) real-life sources of data. In this distribution, 1 occurs as the leading digit about 30% of the time, while larger digits occur in that position less frequently: 9 as the first digit less than 5% of the time. Benford's Law also concerns the expected distribution for digits beyond the first, which approach a uniform distribution. For , the proportion of whose first digit is is approximately . Thus, for instance, should have a first digit of 1 about 30% of the time, but a first digit of 9 only about 5% of the time. The American astronomer Simon Newcomb discovered the law in 1881 that noticed that the first pages of books of logarithms were soiled much more than the remaining pages. In 1938, Frank Benford arrived at the same formula after a comprehensive investigation of listings of data covering a variety of natural phenomena. The law applies to budget, income tax or population figures as well as street addresses of people listed in the book American Men of Science. In the face of such universality of the law, it's quite astonishing that there exists a more general framework - Zipf's...
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...the optimal bidder strategy when values are private is to bid his personal reservation price, regardless of risk aversion. This is a dominant strategy since it maximizes the total available surplus, defined as the difference between the reservation prices of the two highest valuation bidders. This strategy is not optimal when considering common-value auctions, where all bidders value the good similarly but the true value of the good is unknown. The bidder in this case can improve his strategy by bidding lower than his best estimate when: 1) He has less information relative to other bidders about the object’s true value 2) The number of bidders increase 3) He is less confident in his estimate of the true value Winner’s Curse tends to be a problem in price-sealed auctions with common values but not with private values because bidders must estimate the true value of the object without knowing the estimates of others. The graph below1 illustrates that bidders with extreme estimates (right tail of bids distribution) bid values that exceed the best estimate (mean of dotted distribution) and end up paying a price that exceeds the true value, generating negative surplus. In private values, unlike common values, the bidder will not change his valuation when he has knowledge of other bidders’ valuations. The bidder’s reservation price is a function of information and risk -adjusted utility (personal experience) and individuals’ values for the object being auctioned...
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...Probability Distributions True/False 1. The Empirical Rule of probability can be applied to the uniform probability distribution. Answer: False Difficulty: Medium Goal: 1 2. Areas within a continuous probability distribution represent probabilities. Answer: True Difficulty: Medium Goal: 1 3. The total area within a continuous probability distribution is equal to 100. Answer: False Difficulty: Easy Goal: 1 4. The total area within any continuous probability distribution is equal to 1.00 Answer: True Difficulty: Easy Goal: 1 AACSB: REF 5. For any continuous probability distribution, the probability, P(x), of any value of the random variable, X, can be computed. Answer: False Difficulty: Medium Goal: 1 6. For any discrete probability distribution, the probability, P(x), of any value of the random variable, X, can be computed. Answer: True Difficulty: Medium Goal: 1 AACSB: AS 7. The uniform probability distribution's standard deviation is proportional to the distribution's range. Answer: True Difficulty: Medium Goal: 2 8. For any uniform probability distribution, the mean and standard deviation can be computed by knowing the maximum and minimum values of the random variable. Answer: True Difficulty: Medium Goal: 2 9. In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values. Answer:...
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...| Alternative Investment Project | | | | | | | | Content Page: Content | Page | Cover Page | 1 | Content Page | 2 | Executive Summary | 3 | Introduction | 3 | Content of Project | 4 | Conclusion | 9 | Recommendation | 9 | Appendix | 10 | Assignments of work | 19 | Executive Summary: The purpose of the report is to do an in-depth investigation, study and analysis on alternative investments. From the various alternative investments, our team of analyst chose commodities, variable annuities and hedge funds as our subject of interest for the study. Each financial product has its own aims as to cater to the different investment goals to meet the needs of investors. Thus, just by looking at the basis on expensiveness and tax-efficiency, and then from selecting the better one is unwise. We have to look at the overall picture and considering other indispensable factors like risks, liquidity, asset allocation which are equally important. Therefore, our basis of evaluation comprises of various important factors so as to make a robust analysis. Firstly, commodities are a highly demanded investment which is traded using options and futures contract.. Moreover, they are also an element of diversification that investors can lower their vulnerability to market volatility. Despite its high volatility in its prices, it managed to gain a higher return as compared to stocks and bonds. As commodities have a low correlation with bonds...
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...the monthly earnings? X = monthly earnings = revenues – costs = P x M – ( L + 3,995 + 11 x M ) = (P – 11 ) x M – L – 3,995 Which of these quantities are random variables? P M L X = = = = price of prix fixe meal number of meals sold labor cost monthly earnings 3 (X is a function of random variables, so it is a random variable) Assumptions Regarding the Behavior of the Random Variables M P = number of meals sold per month We assume that M obeys a Normal distribution with µ = 3,000 and σ = 1,000 = price of the prix fixe meal We assume that P obeys the following discrete probability distribution Scenario Very healthy market Healthy market Not so healthy market Unhealthy market Price of Prix Fixe Meal $20.00 $18.50 $16.50 $15.00 Probability 0.25 0.35 0.30 0.10 L = labor costs per month We assume that L obeys a uniform distribution with a minimum of $5,040 and maximum of $6,860 4 The Behavior of the Random Variables, cont. X = earnings per month We do not know the distribution of X . We assume, however, that X = (P – 11 ) x M – L – 3,995 Always ask the following questions in any management analysis: • •...
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...SCENARIO ANALYSIS, DECISION TREES AND SIMULATIONS In the last chapter, we examined ways in which we can adjust the value of a risky asset for its risk. Notwithstanding their popularity, all of the approaches share a common theme. The riskiness of an asset is encapsulated in one number – a higher discount rate, lower cash flows or a discount to the value – and the computation almost always requires us to make assumptions (often unrealistic) about the nature of risk. In this chapter, we consider a different and potentially more informative way of assessing and presenting the risk in an investment. Rather than compute an expected value for an asset that that tries to reflect the different possible outcomes, we could provide information on what the value of the asset will be under each outcome or at least a subset of outcomes. We will begin this section by looking at the simplest version which is an analysis of an asset’s value under three scenarios – a best case, most likely case and worse case – and then extend the discussion to look at scenario analysis more generally. We will move on to examine the use of decision trees, a more complete approach to dealing with discrete risk. We will close the chapter by evaluating Monte Carlo simulations, the most complete approach of assessing risk across the spectrum. Scenario Analysis The expected cash flows that we use to value risky assets can be estimated in one or two ways. They can represent a probability-weighted average of cash flows...
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...observations) used in a test, the more accurate the predictions of the behavior of that sample, and smaller the expected deviation in comparisons of outcomes. * As a general principle it means that, in the long run, the average (mean) of a long series of observations may be taken as the best estimate of the 'true value' of a variable. 3.slide * In other words, what is unpredictable and chancy in case of an individual is predictable and uniform in the case of a large group. * This law forms the basis for the expectation of probable-loss upon which insurance premium rates are computed. Also called law of averages. Law of Large Numbers Observe a random variable X very many times. In the long run, the proportion of outcomes taking any value gets close to the probability of that value. The Law of Large Numbers says that the average of the observed values gets close to the mean μ X of X. 4.slide ; Law of Large Numbers for Discrete Random Variables * The Law of Large Numbers, which is a theorem proved about the mathematical model of probability, shows that this model is consistent with the frequency interpretation of probability. 5.slide ; Chebyshev Inequality * To discuss the Law of Large Numbers, we first need an important inequality called the Chebyshev Inequality. * Chebyshev’s Inequality is a formula in probability theory that relates to the distribution of numbers in a set. * This formula is able to prove with little provided information the probability...
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... A 6.75 MT palletizing plant has been set up at Kudremukh, Karnataka which export pellets to various countries. As a result of introduction of pellets in the Ijamudin blast furnace a coke rate decreases 20 -22 kg/tone was expected 8 2. Pellets in the blast furnace charge The use of pellets in the blast furnace charge has a significant effect in the field of the smelting process .But an efficient use of pellet in the charge , depends on the properties of ore, sinter ,coke fluxes etc. i.e. each components of the charging material and the process of smelting. So in order to find the effect of pellets on the important parameters of the blast furnace operation, a study was made on blast furnace no.8 at the “Krivorozhstal” .The pellets were charged along with the iron bearing part of the charge. Sinter and Pellet used in the charge had the following characteristics Table 1 The characteristics of sinter and Pellet Content Sinter...
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...Introduction to Statistics QTM403 Basic Information Program | BBA 3 (Hons.) | Semester | Fall 2015 | Credit Hours | 3 | Pre requisites (if any) | Mathematics | Resource Person | Iftikhar Hussain | Contact information | ihgrw85@gmail.com | Course Description: Important decisions are rarely made by intuition alone. We need to use the data to develop our insights and to support our analysis. Quantitative analysis includes the tools and techniques with which we seek to replicate reality mathematically and statistically. Statistical Techniques are applied in all the functions of business like Operations, Marketing, HR, Finance etc. The aim of this course is to learn when a technique is appropriate and what it can achieve. The emphasis throughout the course is on concepts and reasoning rather than technical details. You should acquire some basic data analysis skills but most importantly, become a more informed and critical producer and user of business Statistical analyses. Learning Objectives: Ser. # | Course Learning Objectives | Link with Program Learning Objectives | 1 | To understand the basic concepts and principles used in Business Statistics. | To inculcate business knowledge and analytical skills in graduates to think decisively in order to develop innovative solutions to problems in a business environment. | 2 | Organizing qualitative and quantitative data into a frequency table, displaying the data through charts...
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...REZENDE* PUC-Rio, Rio de Janeiro, Brazil; and University of Illinois at Urbana–Champaign, Illinois, USA SUMMARY I investigate using the method of ordinary least squares (OLS) on auction data. I find that for parameterizations of the valuation distribution that are common in empirical practice, an adaptation of OLS provides unbiased estimators of structural parameters. Under symmetric independent private values, adapted OLS is a specialization of the method of moments strategy of Laffont, Ossard and Vuong (1995). In contrast to their estimator, here simulation is not required, leading to a computationally simpler procedure. The paper also discusses using estimation results for inference on the shape of the valuation distribution, and applicability outside the symmetric independent private values framework. Copyright 2008 John Wiley & Sons, Ltd. Received 15 September 2006; Revised 1 July 2008 1. INTRODUCTION The field of econometrics of auctions has been successful in providing methods for the investigation of auction data that are well grounded in economic theory and allow for inference on the structure of an auction environment. Today, a researcher has a number of alternative structural methods, especially within the independent private-values paradigm (IPVP); an excellent reference to this literature is the book by Paarsch and Hong (2006). To name a few alternatives, it is possible to use maximum likelihood (Donald and Paarsch, 1996), nonparametric methods (Guerre et al., 2000)...
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...taken from past examinations. The weight of topics in these sample questions is not representative of the weight of topics on the exam. The syllabus indicates the exam weights by topic. Copyright 2013 by the Society of Actuaries and the Casualty Actuarial Society C-09-08 PRINTED IN U.S.A. 1. You are given: (i) Losses follow a loglogistic distribution with cumulative distribution function: bx / θ g F b xg = 1+ bx / θ g γ γ (ii) The sample of losses is: 10 35 80 86 90 120 158 180 200 210 1500 Calculate the estimate of θ by percentile matching, using the 40th and 80th empirically smoothed percentile estimates. (A) (B) (C) (D) (E) Less than 77 At least 77, but less than 87 At least 87, but less than 97 At least 97, but less than 107 At least 107 2. You are given: (i) The number of claims has a Poisson distribution. (ii) (iii) (iv) Claim sizes have a Pareto distribution with parameters θ = 0.5 and α = 6 . The number of claims and claim sizes are independent. The observed pure premium should be within 2% of the expected pure premium 90% of the time. Determine the expected number of claims needed for full credibility. (A) (B) (C) (D) (E) Less than 7,000 At least 7,000, but...
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