...1. Module Name: Introductory Econometrics Code: P12205 Credits: 10 Semester: Spring 2011/12 Delivery: 16 one-hour lectures + 4 one-hour workshops Aims: The main aims of this module are: to introduce students to the principles, uses and interpretation of regression analysis most commonly employed in applied economics; to provide participants with sufficient knowledge of regression methods to critically evaluate and interpret empirical research. On completion of this module students should be able to: demonstrate understanding of the assumptions and properties underlying regression analysis and the principle of ‘least squares’; interpret and manipulate the coefficients of multiple regression and performance criteria; conduct diagnostic checking of the validity of regression equations coefficients; appreciate the problems of misspecification, multicollinearity, heteroscedasticity and autocorrelation. Content: 1. Simple Regression Analysis 2. Multiple Regression Analysis 3. Dummy Variables 4. Heteroscedasticity 5. Autocorrelation Main Textbook: Dougherty, C. (2011). Introduction to Econometrics, 4th edition, Oxford. 2. Module Name: Computational Finance Code: P12614 Credits: 10 Semester: Spring 2011/12 Programme classes: 12 1-2 hour lectures/workshops Aims: The module aims to describe and analyse the general finance topics and introduces students to implement basic computational approaches to financial problems using Microsoft Excel. It stresses...
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...Contents No. | Title | Page | 1 | Introduction | 2 | 2 | Part 1 | 6 | 3 | Part 2 | 8 | 4 | Part 3 | 10 | 5 | Part 4 | 13 | 6 | Part 5 | 17 | 7 | Further Exploration | 21 | 8 | Reflection | 22 | Introduction Moral Values: I have learned many moral values while completing this assignment. Better still, I got to know about the importance of applying these moral values into our daily lives. The first moral value is to cooperate with other people. The strategies and solutions of the questions in this project work were discussed among me and a group of friends. This makes things easier and saved a lot of time. The management of time is also important to complete this project work. Other than this assignment, I have homework, extra co curricular activities and tuition classes to attend. Thus a good management of time is essential for me to complete this given task and not to disrupt my daily activities. Perseverance has taught me to be steady and persistent in doing something. In spite of many difficulties I faced throughout the whole procedure I learned that giving up is just not right solution. Obstacles and discouragement should be endured the course of action should be held on with unyielding determination to see obtain sweet fruit of success. I had also learned to appreciate the beauty of mathematics. Waxing eloquently on the basic importance of Mathematics in human life, Roger Bacon (1214-1294), an English Franciscan friar, philosopher, scientist...
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...TEMPLATE PROBABILITY AND STATISTICS Draft By Paul Chege Version 19.0, 23rd March, 2007 C. TEMPLATE STRUCTURE I. INTRODUCTION 1. TITLE OF MODULE Probability and Statistics 2. PREREQUISITE COURSES OR KNOWLEDGE Secondary school statistics and probability. 3. TIME The total time for this module is 120 study hours. 4. MATERIAL Students should have access to the core readings specified later. Also, they will need a computer to gain full access to the core readings. Additionally, students should be able to install the computer software wxMaxima and use it to practice algebraic concepts. 5. MODULE RATIONALE Probability and Statistics, besides being a key area in the secondary schools’ teaching syllabuses, it forms an important background to advanced mathematics at tertiary level. Statistics is a fundamental area of Mathematics that is applied across many academic subjects and is useful in analysis in industrial production. The study of statistics produces statisticians that analyse raw data collected from the field to provide useful insights about a population. The statisticians provide governments and organizations with concrete backgrounds of a situation that helps managers in decision making. For example, rate of spread of diseases, rumours, bush fires, rainfall patterns, and population changes. On the other hand, the study of probability helps decision making in government agents...
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...Chapter 1 Discrete Probability Distributions 1.1 Simulation of Discrete Probabilities Probability In this chapter, we shall first consider chance experiments with a finite number of possible outcomes ω1 , ω2 , . . . , ωn . For example, we roll a die and the possible outcomes are 1, 2, 3, 4, 5, 6 corresponding to the side that turns up. We toss a coin with possible outcomes H (heads) and T (tails). It is frequently useful to be able to refer to an outcome of an experiment. For example, we might want to write the mathematical expression which gives the sum of four rolls of a die. To do this, we could let Xi , i = 1, 2, 3, 4, represent the values of the outcomes of the four rolls, and then we could write the expression X 1 + X 2 + X 3 + X4 for the sum of the four rolls. The Xi ’s are called random variables. A random variable is simply an expression whose value is the outcome of a particular experiment. Just as in the case of other types of variables in mathematics, random variables can take on different values. Let X be the random variable which represents the roll of one die. We shall assign probabilities to the possible outcomes of this experiment. We do this by assigning to each outcome ωj a nonnegative number m(ωj ) in such a way that m(ω1 ) + m(ω2 ) + · · · + m(ω6 ) = 1 . The function m(ωj ) is called the distribution function of the random variable X. For the case of the roll of the die we would assign equal probabilities or probabilities 1/6 to each of the outcomes....
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...Queuing Theory Most restaurants want to provide an ideal level of service wherein they could serve their customers at the least minimum time. However, as the restaurant established its name to the public, it makes a great queuing or waiting line that most of the customers do not want. Not all restaurants desire for queue since it could make confusions to them and because of their losses from the customers who go away and dissatisfied. For some time, adding chairs and tables are not enough to solve the queuing problem. In the case of Tamagoya Noodle House, they have this principle of serving the customer with their high quality ramen regardless of the number of customers. In short, they are more on the quality than the quantity; not on the profit side but rather on the quality side. But because they really want to serve more customers especially those ramen lovers who came from far places, they want to solve these queuing problems. Service time distribution Arrivals Customer 3 Customer 2 Customer 1 Service Facility Queue Fig. 1 Queuing System Configuration Assumptions of the model: Since Tamagoya Noodle House uses a Single-Channel, Single-Phase model in order to avoid confusion of customer’s order. The model we used assumes that seven conditions exist: 1. Arrivals are served on a First-in, First-out basis. Though some of customers who ordered less and or senior citizens were prioritized to be served first. 2. Every customer...
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...Unit 2 DB Subjective Probability “ A probability derived from an individual's personal judgment about whether a specific outcome is likely to occur. Subjective probabilities contain no formal calculations and only reflect the subject's opinions and past experience.” (investopedia.com, 2013) There are three elements of a probability which combine to equal a result. There is the experiment ,the sample space and the event (Editorial board, 2012). In this case the class is the experiment because the process of attempting it will result in a grade which could vary from an A to F. The different grades that can be achieved in the class are the sample space. The event or outcome is the grade that will be received at the end of the experiment. I would like to achieve an “A” in this class but due to my lack of experience in statistical analysis, my hesitation towards advanced mathematics, and the length of time it takes for me to complete my course work a C in this class may be my best result. I have a 1/9 chance or probability to receive an “A” in the data range presented to me which is (A,A-,B,B-,C,C-,D,D- AND F). By the grades that have been posted I would say that the other students have a much better chance of receiving a better grade than mine. I have personally use subjective probability in my security guard business in bidding on contracts based on the clients involved , the rates that I charge versus the rates other companies charge and the amount of work involved...
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...Fin 700 Tianqi Sun Dr. Al. Barzykowsi Dec. 19, 2015 Short Paper - Statistical Methods This paper talks about statistical methods. Statistical data indicates that the agency 's approach is characterized by its population by inference Presented from a representative sample of the population views. As scientists rarely observed throughout Crowd, sampling and statistical inference is essential. This paper discusses some of the general principles Visualization of planning experiments and data. Then, a strong focus on the appropriate choice Standard statistical models and statistical inference methods. First of all, the Standard Model described. These models, in order to apply interval estimation and hypothesis testing parameters Also described, including the next two sample cases, when the purpose of comparing two or more of the population For their means and variances. Secondly, non-parametric inference tests are also described in the case where the data Sample distribution is not compatible with standard parameter distribution. Thirdly, using multiple resampling methods Computer -generated random sample finally introduced the characteristics of the distribution and estimate Statistical inference. The method of multivariate data processing of the following sections involved. method Clinical trials also briefly review process. Finally, the last section of statistical computer software discussion And through the collection of citations to adapt to different levels of expertise...
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...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 of the probability of a successful closure of the major purchase is 0.5. Regional sales of OB1 would be boosted by the successful closure, and the management of Blanket Systems has estimated the regional sales potential (in addition to the major purchase), as shown in the table below. If major purchase Probability 0.2 0.3 0.3 0.2 If no major purchase Sales Probability 1000 0.25 2000 0.25 3000...
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...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 of outliers existing at a certain interval. 6.slide * Given X is a random variable, A stands for the mean of the set, K is the number of standard deviations, and Y is the value of the standard deviation, the formula reads as follows: *...
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...philosophical ontology, and forced the philosophical community to rethink the way it conceptualizes “natural” laws and our own intuitions regarding our existence. Is it possible that all of our ideas about the world in which we live are false, and are simply the result of our own desire to believe that we are “real”? Even more troubling, if we are living in a computer simulation, is it possible that the simulation might be shut off at any moment? In this paper, I plan to do two things. First, I hope to consider what conclusions we might draw from Bostrom’s argument, and what implications this might have for how we affect our lives. Second, I plan to discuss a possible objection to Bostrom’s argument, and how this might affect our personal probability for the possibility that we are living in a computer simulation. Bostrom begins his argument by making a few assumptions necessary to the probabilistic claims he makes. The first is substrate-independence. This is simply the claim that if we were able to model the mind with enough detail, then we would be able to create artificial minds capable of thought in the same way that we are. He goes further to assume that, if we were able to simulate the entire world in sufficient detail, and feed this world into the artificial minds we have created in the form of sensory inputs, the artificial minds would be incapable of determining that they were in a simulation, unless they were given explicit knowledge of it by the creators...
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...Statistics is the study of the collection, organization, analysis, interpretation and presentation of data.[1][2] It deals with all aspects of data, including the planning of data collection in terms of the design of surveys and experiments.[1] The word statistics, when referring to the scientific discipline, is singular, as in "Statistics is an art."[3] This should not be confused with the word statistic, referring to a quantity (such as mean or median) calculated from a set of data,[4] whose plural is statistics ("this statistic seems wrong" or "these statistics are misleading"). Some consider statistics a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data,[5] while others consider it a branch of mathematics[6] concerned with collecting and interpreting data. Because of its empirical roots and its focus on applications, statistics is usually considered a distinct mathematical science rather than a branch of mathematics.[7][8] Much of statistics is non-mathematical: ensuring that data collection is undertaken in a way that produces valid conclusions; coding and archiving data so that information is retained and made useful for international comparisons of official statistics; reporting of results and summarised data (tables and graphs) in ways comprehensible to those who must use them; implementing procedures that ensure the privacy of census information. Statisticians improve data quality by developing...
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...Classical Probabilistic Models and Conditional Random Fields Roman Klinger Katrin Tomanek Algorithm Engineering Report TR07-2-013 December 2007 ISSN 1864-4503 Faculty of Computer Science Algorithm Engineering (Ls11) 44221 Dortmund / Germany http://ls11-www.cs.uni-dortmund.de/ Classical Probabilistic Models and Conditional Random Fields Roman Klinger∗ Katrin Tomanek∗ Fraunhofer Institute for Algorithms and Scientific Computing (SCAI) Schloss Birlinghoven 53754 Sankt Augustin, Germany Jena University Language & Information Engineering (JULIE) Lab F¨rstengraben 30 u 07743 Jena, Germany Dortmund University of Technology Department of Computer Science Chair of Algorithm Engineering (Ls XI) 44221 Dortmund, Germany katrin.tomanek@uni-jena.de roman.klinger@scai.fhg.de roman.klinger@udo.edu Contents 1 Introduction 2 2 Probabilistic Models 2.1 Na¨ Bayes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ıve 2.2 Hidden Markov Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Maximum Entropy Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4 5 6 3 Graphical Representation 10 3.1 Directed Graphical Models . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2 Undirected Graphical Models . . . . . . . . . . . . . . . . . . . . . . . . . 13 4 Conditional Random Fields 4.1 Basic Principles . . . . . . . . 4.2 Linear-chain CRFs . . . . . . 4.2.1 Training . . . ...
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...DECISION THEORY & DECISION TREES(Decision making under risk) Janet Kim, president Kim Manufacturing, Inc., is considering whether or not to build more manufacturing plants in Wisconsin. She has developed the following pay-off table for her decision: Payoff in dollars Alternative Build large plant Build small plant Don’t build Market probabilities Favorable Market 400,000 80,000 0 0.4 Unfavorable Market -300,000 -10,000 0 0.6 (a) Use the expected monetary value approach to determine the decision that Kim should make. (b) Use the expected opportunity loss (regret) approach to determine the decision that Kim should make. (c) What is the expected value of perfect information? Class Example 2 (Decision making under uncertainty) Even though independent gas stations have been having a difficult time, Susan Solomon has been thinking about starting her own independent gasoline station. Susan’s problem is to decide how large her station should be. The annual returns depend on both the size of her station and a number of market factors related to the oil industry and demand for gasoline. After a careful analysis Susan has developed the following table: Size of gas station Small Medium Large Very large Payoff in dollars Good Market 50,000 80,000 100,000 300,000 Fair Market 20,000 30,000 30,000 25,000 Poor Market -10,000 -20,000 -40,000 -160,000 (a) What is the Maximax (optimistic) decision? (b) What is the Maximin (pessimistic) decision? (c) What is the criterion of realism decision...
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...this 6.3 Probabilities Using Counting TechniquesThis is a featured page In a number of different situations, it is not easy to determine the outcomes of an event by counting them individually. Alternatively, counting techniques that involve permutations and combinations are helpful when calculating theoretical probabilities. This section will examine methods for determining theoretical probabilities of successive or multiple events. Permutation? or Combination? The following flow chart will help determine which formula is suitable for any given question. By simply following a series of "yes" or "no" questions, the appropriate formula can be determined. Flow Ex. 1 - Using Permutations: 6.3 Probabilities Using Counting Techniques - MDM4U1@FMG 6.3 Probabilities Using Counting Techniques - MDM4U1@FMG The specific outcome of Mike starting in lane 1 and the other two starting in lane 2 and lane 3 can only happen one way, so n(A) = 1. Therefore, 6.3 Probabilities Using Counting Techniques - MDM4U1@FMG The probability that Mike will start in the first lane next to his other brothers in lane 2 and 3 is approximately 0.00101. Ex. 1(a) - Using Permutations: Exactly Three People form a line at a grocery store. What is the probability that they will line up in descending order of age? (I.e. oldest, middle and youngest) →Solution using the blank like method: n(A): # of ways they will line up in descending order of age, thus: 6.3 Probabilities Using Counting...
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...Chapter 6 Statistical Process Control 6.0 Introduction One of the axioms or truisms in law of nature is “No two items of any category at any instant in the universe are the same”. Manufacturing process is no exception to it. It means that variability is part of life and is an inherent property of any process. Measuring, monitoring and managing are rather engineers’ primary job in the global competition. A typical manufacturing scenario can be viewed as shown in the Figure 6.1. That is if one measures the quality characteristic of the output, he will come to know that no two measured characteristics assume same value. This way the variablility conforms one of the axioms or truisms of law of nature; no two items in the universe under any category at any instant will be exactly the same. In maunufacturing scenario, this variability is due to the factors (Random variables) acting upon the input during the process of adding value. Thus the process which is nothing but value adding activity is bound ot experience variability as it is inherent and integral part of the process. Quality had been defined in many ways. Quality is fitness for use is the most common way of looking at it. This fitness for use is governed by the variability. In a maufacturing scenario, despite the fact that a machine operator uses the same precision methods and machines and endeavours to produce identical parts, but the finished products will show a definite variablity. The variability of a product...
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