...Paper Presented to: Edmar Orata Probability by: Jirolyn Fabro Miguel Angelo Rosales March 15, 2012 I - Introduction II - Interpretations III - Etymology IV - History V - Applications 1. Weather Forecasting 2. Batting Average 3. Winning the Lottery 4. VI - Discussion VII - I-Introduction Probability is the ratio of the number of ways an event can occur to the number of possible outcomes. Probability is expressed as a fraction or decimal from 0 to 1. Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we are not certain.[1] The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The certainty we adopt can be described in terms of a numerical measure and this number, between 0 and 1, we call probability. [2] The higher the probability of an event, the more certain we are that the event will occur. Thus, probability in an applied sense is a measure of the likeliness that a (random) event will occur. The concept has been given an axiomatic mathematical derivation in probability theory, which is used widely in such areas of study as mathematics, statistics, finance, gambling, science, artificial intelligence/machine learning and philosophy to, for example, draw inferences about the likeliness of events. Probability is used to describe the underlying mechanics...
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...Case Study1: The World Cup Case Study1: The World Cup Let t=true odds Let b= Implied Fair odds Let p=proability of 'implied' fair bet odds Rank on 6/10/2010 1 2 3 4 5 6 7 8 9 10 11 12 13 13 13 16 16 16 19 19 21 21 23 23 25 26 27 27 29 30 31 31 Team Spain Brazil Argentina England Holland Germany Italy France Portugal Ivory Coast Serbia Chile Paraguay Mexico U.S.A. Ghana Cameroon Uruguay Denmark Nigeria South Africa Australia Greece Switzerland Slovakia South Korea Slovenia Japan Algeria Honduras New Zealand North Korea Odds (b) on 6/10/2010 => Wager/Bet P(win) P(Lose) fairbet=> => => 4 4.5 6.5 7.5 9 14 16 20 25 50 60 70 80 80 80 100 100 100 125 125 150 150 200 200 225 250 300 300 600 1000 2000 2000 => => => => => => => => => => => => => => => => => => => => => => => => => => => => => => => => 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 1-p 4(p)=1(1-p) 4.5(p)=1(1-p) 6.5(p)=1(1-p) 7.5(p)=1(1-p) 9(p)=1(1-p) 14(p)=1(1-p) 16(p)=1(1-p) 20(p)=1(1-p) 25(p)=1(1-p) 50(p)=1(1-p) 60(p)=1(1-p) 70(p)=1(1-p) ...
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...Applied Statistical Methods Larry Winner Department of Statistics University of Florida February 23, 2009 2 Contents 1 Introduction 1.1 Populations and Samples . . . . . . . . . . . 1.2 Types of Variables . . . . . . . . . . . . . . . 1.2.1 Quantitative vs Qualitative Variables 1.2.2 Dependent vs Independent Variables . 1.3 Parameters and Statistics . . . . . . . . . . . 1.4 Graphical Techniques . . . . . . . . . . . . . 1.5 Basic Probability . . . . . . . . . . . . . . . . 1.5.1 Diagnostic Tests . . . . . . . . . . . . 1.6 Exercises . . . . . . . . . . . . . . . . . . . . 7 7 8 8 9 10 12 16 20 21 25 25 29 29 29 32 32 32 32 32 35 35 37 38 38 39 40 42 42 44 48 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Random Variables and Probability Distributions 2.1 The Normal Distribution . . . . . . . . . . . . . . . . . . 2.1.1 Statistical Models . . . . . . . . . . . . . . . . . 2.2 Sampling Distributions and the Central Limit Theorem 2.2.1 Distribution of Y . . . . . . . . . . . . . . . . . . 2.3 Other Commonly Used Sampling Distributions . . . . . 2.3.1 Student’s...
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...PERCENTAGES: THE MOST USEFUL STATISTICS EVER INVENTED Thomas R. Knapp © 2010 "Eighty percent of success is showing up." - Woody Allen “Baseball is ninety percent mental and the other half is physical.” - Yogi Berra "Genius is one percent inspiration and ninety-nine percent perspiration." - Thomas Edison Preface You know what a percentage is. 2 out of 4 is 50%. 3 is 25% of 12. Etc. But do you know enough about percentages? Is a percentage the same thing as a fraction or a proportion? Should we take the difference between two percentages or their ratio? If their ratio, which percentage goes in the numerator and which goes in the denominator? Does it matter? What do we mean by something being statistically significant at the 5% level? What is a 95% confidence interval? Those questions, and much more, are what this book is all about. In his fine article regarding nominal and ordinal bivariate statistics, Buchanan (1974) provided several criteria for a good statistic, and concluded: “The percentage is the most useful statistic ever invented…” (p. 629). I agree, and thus my choice for the title of this book. In the ten chapters that follow, I hope to convince you of the defensibility of that claim. The first chapter is on basic concepts (what a percentage is, how it differs from a fraction and a proportion, what sorts of percentage calculations are useful in statistics...
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...Chapter 1: The Role of BR I. The Nature of Research A. BR defined B. Applied & basic BR C. The scientific method II. Managerial Value of BR A. Identifying problems or opportunities B. Diagnosing & assessing problems or opportunities C. Selecting & implementing a course of action D. Evaluating the course of action III. When is BR Needed? A. Time constraints B. Availability of data C. Nature of the decision D. Benefits vs costs IV. BR In The 21st Century A. Communication technologies B. Global BR Chapter 3: Theory Building I. Introduction A. What is a theory? B. What are the goals of theory? II. Research Concepts, Constructs, Proposition, Variables & Hypotheses A. Research concepts & constructs B. Research proposition & hypotheses III. Understanding Theory A. Verifying theory B. Theory building Chapter 5: The Human Side of BR: Organizational & Ethical Issue I. Introduction II. Ethical issue in BR A. Ethical qs are philosophical qs B. General rights & obligation of concerned parties C. Rights & obligation of the research participant * The obligation to be truthful * Participants’ right to privacy * Active & Passive research * Deception in research designs & the right to be informed * Experiment designs * Descriptive research * Protection from harm D. Rights & obligation of the...
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...than useless — plus, we're subject to cognitive biases, those annoying glitches in our thinking that cause us to make questionable decisions and reach erroneous conclusions. Here are a dozen of the most common and pernicious cognitive biases that you need to know about. Before we start, it's important to distinguish between cognitive biases and logical fallacies. A logical fallacy is an error in logical argumentation (e.g. ad hominem attacks, slippery slopes, circular arguments, appeal to force, etc.). A cognitive bias, on the other hand, is a genuine deficiency or limitation in our thinking — a flaw in judgment that arises from errors of memory, social attribution, and miscalculations (such as statistical errors or a false sense of probability). Some social psychologists believe our cognitive biases help us process information more efficiently, especially in dangerous situations. Still, they lead us to make grave mistakes. We may be prone to such errors in judgment, but at least we can be aware of them. Here are some important ones to keep in mind. Confirmation Bias We love to agree with people who agree with us. It's why we only visit websites that express our political opinions, and why we mostly hang around people who hold similar views and tastes. We tend to be put off by individuals, groups, and news sources that make us feel uncomfortable or insecure about our views — what the behavioral psychologist B. F. Skinner called cognitive dissonance. It's this preferential...
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...Profitable Sports Gambling Fabián Enrique Moya B.Sc., Anáhuac University, 2001 Project Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science Statistical Methodology for by Department of Statistics and Actuarial Science Faculty of Science in the SIMON FRASER UNIVERSITY Summer 2012 © Fabián Enrique Moya 2012 All rights reserved. However, in accordance with the Copyright Act of Canada, this work may be reproduced, without authorization, under the conditions for “Fair Dealing.” Therefore, limited reproduction of this work for the purposes of private study, research, criticism, review and news reporting is likely to be in accordance with the law, particularly if cited appropriately. Approval Name: Degree: Title of Project: Examining Committee: Fabián Enrique Moya Master of Science (Applied Statistics) STATISTICAL METHODOLOGY FOR PROFITABLE SPORTS GAMBLING Chair: Dr. Carl Schwarz, Professor Dr. Tim Swartz Senior Supervisor Professor Dr. Paramjit Gill Committee Member Professor, Department of Mathematics and Statistics University of British Columbia – Okanagan Dr. Joan Hu External Examiner Professor Date Defended/Approved: July 24, 2012 ii Partial Copyright Licence The author, whose copyright is declared on the title page of this work, has granted to Simon Fraser University the right to lend this thesis, project or extended essay to users if the Simon Fraser University Library, and to make partial or...
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...Twenty20 league worldwide. In 2010, the IPL became the first sporting event to be broadcast live on YouTube. The brand value of the 2014 Indian Premier League was estimated to be US$7.2 billion. Cricket is one of the game which includes lots of betting and predictions. Due to this reason many researchers try out different methods to introduce new models to predict the result of the match. In this report we are making an attempt to predict the outcomes of some of the most important matches that will be played in the Indian Premier league in the forth coming year from April 8 to May 29. We use the Poisson distribution to create a model with which we will be able to predict (1) if there is any Home ground advantage to the home team, 2) Probability of the total runs per over that will be scored in the match by individual teams, finally we will predict which team will win the match using this model. We use the data from the previous seasons 2014 and 2015 to predict these matches. This model introduces you to predicting individual matches which can be further developed into an advanced model with which you can predict the season results and individual scores of a single batsmen. Introduction to Cricket and Betting: Cricket is the second most popular game in the world only next to football. The latest form of cricket is the Twenty20 or T20 cricket. It involves two teams with each team...
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...Differential Effects of Cigarette Price on Youth Smoking Intensity 1Department of Economics, University of Illinois at Chicago 2Health Research and Policy Centers, University of Illinois at Chicago 3Health Economics Program, National Bureau of Economic Research ACKNOWLEDGEMENTS Support for this research was provided by grants from The Robert Wood Johnson Foundation (ImpacTeen – A Policy Research Partnership to Reduce Youth Substance Use) and the Centers for Disease Control and Prevention (Price, Availability and Youth Tobacco Use) to the University of Illinois at Chicago. We thank Lloyd D. Johnston and Patrick J. O’Malley of the University of Michigan’s Institute for Social Research for providing us with selected data from the 1992, 1993 and 1994 Monitoring the Future Surveys. The Monitoring the Future Project is supported by a grant from the National Institute on Drug Abuse Abstract Objectives: Data from the 1992, 1993, and 1994 Monitoring the Future Surveys were used to investigate the differential effects of cigarette price on the intensity of youth cigarette smoking. Methods: Respondents are classified into nonsmokers; individuals who smoked less than one cigarette per day; individuals who smoked one to five cigarettes per day; individuals who smoked one-half pack a day; and individuals who smoked one pack or more a day. A Threshold of Change Model was estimated with information on cigarette prices as the main explanatory variables. Results: Dummy variables...
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...Public Health and Health Care Organizations MODERN MANAGEMENT APPROACHES TO CREATE VALUE MARKETING STRATEGIC MANAGEMENT Organizations will always end up somewhere…. “Cheshire Puss, …would you tell me, please, which way I ought to go from here?” “That depends a good deal on where you want to get to,” said the Cat. “I don’t much care where ----”said Alice. “Then it doesn’t matter much which way you go,” said the Cat. “---So long as I get somewhere,” Alice added as an explanation. “Oh, you’re sure to do that,” said the Cat. Lewis Carroll, Alice’s Adventures in Wonderland Strategic Management “Planning amid the chaos” • Assessment • Visioning and strategic thinking • Hands-on, nitty-gritty planning Strategic Planning vs. Strategic Thinking Strategic Planning • Programming • Analysis • Rearranging categories • Calculating Strategic Thinking • New visions • Synthesis • Inventing new categories • Committing = Strategic Management Strategic Management Process • Situational Analysis ü Mission, vision, values, and objectives ü Situation Assessment ü External/Internal Environment • Strategy Formulation • Strategy Implementation • Strategy Evaluation & Control SWOT Analysis Skills & Abilities Funding & Resources Commitment Networks & Contacts Existing Activities Other Organizations Politics & Policy Trends & Forces Mobilizing for Action through Planning and Partnerships (MAPP) Five Types of Strategy 1. Directional: What are...
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...inferential statistics Know the properties of & be able to identify or provide examples of quantitative vs. categorical variables BASIC CONCEPTS (CHAPTER 2 – MUNRO E-BOOK) Know the definition of data, individuals, variables, independent variable, dependent variable, random assignment, treatment group, and control group. Know the properties of the 4 levels of measurement (nominal, ordinal, interval, ratio) Know the properties of discrete and continuous variables Know and understand the properties that distinguish experimental methods from correlational methods DISPLAYING DATA (CHAPTER 2 – MUNRO E-BOOK) Know what a distribution is and why examining a distribution can be helpful/useful Know how to interpret information from: Simple frequency distributions (grouped & ungrouped*) Relative frequency distributions (proportions* & percents*) Cumulative frequency distributions* Histograms Bar graphs* Stem-and-leaf displays You also should know how to construct those with an * beside them Know the definition of percentile rank Be able to identify and/or describe different shapes of distributions: Normal, symmetrical, skewed, unimodal, & bimodal distributions CENTRAL TENDENCY (CHAPTER 2 – MUNRO E-BOOK) Understand conceptually each of the 3 measures of central tendency: Mode, Median & Mean Know how to compute the mean, median, & mode Be sure to know how to find the median when: N is odd N is even Know how to determine the shape of a distribution based on info about central tendency (& vice...
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...INTEGERS Definition Integers are defined as: all negative natural numbers , zero , and positive natural numbers . Note that integers do not include decimals or fractions - just whole numbers. Even and Odd Numbers An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. An even number is an integer of the form , where is an integer. An odd number is an integer that is not evenly divisible by 2. An odd number is an integer of the form , where is an integer. Zero is an even number. Addition / Subtraction: even +/- even = even; even +/- odd = odd; odd +/- odd = even. Multiplication: even * even = even; even * odd = even; odd * odd = odd. Division of two integers can result into an even/odd integer or a fraction. IRRATIONAL NUMBERS Fractions (also known as rational numbers) can be written as terminating (ending) or repeating decimals (such as 0.5, 0.76, or 0.333333....). On the other hand, all those numbers that can be written as non-terminating, non-repeating decimals are non-rational, so they are called the "irrationals". Examples would be ("the square root of two") or the number pi (~3.14159..., from geometry). The rationals and the irrationals are two totally separate number types: there is no overlap. Putting these two major classifications, the rationals and the irrationals, together in one set gives you the "real" numbers. POSITIVE AND NEGATIVE NUMBERS A positive number is...
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...PROBABILITY SEDA YILDIRIM 2009421051 DOKUZ EYLUL UNIVERSITY MARITIME BUSINESS ADMINISTRATION CONTENTS Rules of Probability 1 Rule of Multiplication 3 Rule of Addition 3 Classical theory of probability 5 Continuous Probability Distributions 9 Discrete vs. Continuous Variables 11 Binomial Distribution 11 Binomial Probability 12 Poisson Distribution 13 PROBABILITY Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions. In common usage, the word "probability" is used to mean the chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%. The analysis of events governed by probability is called statistics. There are several competing interpretations of the actual "meaning" of probabilities. Frequentists view probability simply as a measure of the frequency of outcomes (the more conventional interpretation), while Bayesians treat probability more subjectively as a statistical procedure that endeavors to estimate parameters of an underlying distribution based on the observed distribution. The conditional probability of an event A assuming that B has occurred, denoted ,equals The two faces of probability introduces a central ambiguity which has been around for 350 years and still leads to disagreements about...
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...Problem Books in Mathematics Edited by P. Winkler Problem Books in Mathematics Series Editors: Peter Winkler Pell’s Equation by Edward J. Barbeau Polynomials by Edward J. Barbeau Problems in Geometry by Marcel Berger, Pierre Pansu, Jean-Pic Berry, and Xavier Saint-Raymond Problem Book for First Year Calculus by George W. Bluman Exercises in Probability by T. Cacoullos Probability Through Problems by Marek Capi´ski and Tomasz Zastawniak n An Introduction to Hilbert Space and Quantum Logic by David W. Cohen Unsolved Problems in Geometry by Hallard T. Croft, Kenneth J. Falconer, and Richard K. Guy Berkeley Problems in Mathematics (Third Edition) by Paulo Ney de Souza and Jorge-Nuno Silva The IMO Compendium: A Collection of Problems Suggested for the International Mathematical Olympiads: 1959–2004 by Duˇan Djuki´, Vladimir Z. Jankovi´, Ivan Mati´, and Nikola Petrovi´ s c c c c Problem-Solving Strategies by Arthur Engel Problems in Analysis by Bernard R. Gelbaum Problems in Real and Complex Analysis by Bernard R. Gelbaum (continued after subject index) Wolfgang Schwarz 40 Puzzles and Problems in Probability and Mathematical Statistics Wolfgang Schwarz Universit¨ t Potsdam a Humanwissenschaftliche Fakult¨ t a Karl-Liebknecht Strasse 24/25 D-14476 Potsdam-Golm Germany wschwarz@uni-potsdam.de Series Editor: Peter Winkler Department of Mathematics Dartmouth College Hanover, NH 03755 USA Peter.winkler@dartmouth.edu ISBN-13: 978-0-387-73511-5 e-ISBN-13: 978-0-387-73512-2 ...
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...For Students Solutions to Odd-Numbered End-of-Chapter Exercises * Chapter 2 Review of Probability 2.1. (a) Probability distribution function for Y Outcome (number of heads) | Y 0 | Y 1 | Y 2 | Probability | 0.25 | 0.50 | 0.25 | (b) Cumulative probability distribution function for Y Outcome (number of heads) | Y 0 | 0 Y 1 | 1 Y 2 | Y 2 | Probability | 0 | 0.25 | 0.75 | 1.0 | (c) . Using Key Concept 2.3: and so that 2.3. For the two new random variables and we have: (a) (b) (c) 2.5. Let X denote temperature in F and Y denote temperature in C. Recall that Y 0 when X 32 and Y 100 when X 212; this implies Using Key Concept 2.3, X 70oF implies that and X 7oF implies 2.7. Using obvious notation, thus and This implies (a) per year. (b) , so that Thus where the units are squared thousands of dollars per year. (c) so that and thousand dollars per year. (d) First you need to look up the current Euro/dollar exchange rate in the Wall Street Journal, the Federal Reserve web page, or other financial data outlet. Suppose that this exchange rate is e (say e 0.80 Euros per dollar); each 1 dollar is therefore with e Euros. The mean is therefore e C (in units of thousands of Euros per year), and the standard deviation is e C (in units of thousands of Euros per year). The correlation is unit-free, and is unchanged. 2.9. | | Value of Y | Probability Distribution of X | | | 14 | 22 | 30 | 40 | 65 | | | Value of X | 1 |...
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