...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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...Written Assignment Unit 6________________________________________ 1) The first task is to review some information that might be useful later: a) Write a brief definition of the word "quartile" as we have used it in previous weeks. Be sure to provide a citation: A quartile is the number that spits a set of data into quarters; thus, there is the first quartile, the second (median) and the third quartile (Yakir, 2011, p.g 32). b) Write a brief definition of the word "quantile" as it might be used in statistics. Be sure to provide a citation (do not cut and paste... use your own words to summarize what you discovered): A quantile is refers to aa set of values that split an ordered set of data, into equal parts. For instance, a quartile is a...
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...claim during the year. 15 policyholders are selected randomly. What is the probability that at least 3 of them submitted a claim the previous year? 3. When a class interval is expressed as 100 up to 200, _________________________. 4. A coffee manufacturer is interested in whether the mean daily consumption of regular-coffee drinkers is less than that of decaffeinated-coffee drinkers. A random sample of 50 regular-coffee drinkers showed a mean of 4.35 cups per day, with a standard deviation of 1.2 cups per day. A sample of 40 decaffeinated coffee drinkers showed a mean of 5.84 cups per day, with a standard deviation of 1.36 cups per day. What is your computed z-statistic? 5. You perform a hypothesis test at the .05 level of significance. Your computed p-value turns out to .042. What is your decision about the hypothesis? 6. In a distribution, the second quartile corresponds with the __________. 7. The MacBurger restaurant chain claims that the waiting time of customers for service is normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. The quality-assurance department found in a sample of 50 customers at the Warren Road MacBurger that the mean waiting time was 2.75 minutes. When you perform a test of hypothesis, what would be the resulting p-value? 8. The first card selected from a standard 52-card deck was a king. If it is returned to the deck, what is the probability that a king...
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...QNT-351 Discussion Question Responses * DQ#1: What is the importance of statistics in business decision making? Describe a business situation where statistics was used in making a decision. 1. Using statistics to evaluate the performance of your business. Taking all factors into account, determine whether you are making or losing money. In addition, determine the trend of your business. For example, determine whether, over time, you are making more or less profit (or loss). Track the share of the market that your business holds, and how this changes over time. Evaluate all these factors for each product type, even each model, in your company's line. The statistics to use here are simple line and bar graphs of data. These data can alert you to where you need to change aspects of your business, and how quickly you have to make that change. Furthermore, statistics are an excellent way to determine how you should allocate your resources to increase sales. Sales in a given market are a result of a number of factors, such as pricing, the size of the sales force, and the type and number of advertisements placed. However, these factors will not be equally important for every product. You would use multiple regressions to determine which of these factors are most important, and how much changing your asset allocation (for example, the size of the sales force) will change sales. 2. Statistics: The science of collecting, organizing, and analyzing data. Descriptive Statistics...
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...Planning and conducting a study • Anticipating Patterns: Exploring random phenomena using probability and simulation • Statistical Inference: Estimating population parameters and testing hypotheses Students who successfully complete the course and examination may receive credit and/or advanced placement for a one-semester introductory college statistics course. Textbook: The Practice of Statistics, 3rd ed. (2008) by Yates, Moore and Starnes (Freeman Publishers) Calculator needed: TI-83 Graphing Calculator (Rentals Available) TI-83+, TI-84, TI-84+ are acceptable calculators as well Note: Any other calculator may/may not have statistical capabilities, and the instructor shall assist whenever possible, but in these instances, the student shall have sole responsibility for the calculator’s use and application in this course. AP STATISTICS Textbook: The Practice of Statistics, 3rd edition by Yates, Moore and Starnes Preliminary Chapter – What Is Statistics? (2 Days) A. Where Do Data Come From? 1. Explain why we should not draw conclusions based on personal experiences. 2. Recognize whether a study is an experiment, a survey, or an observational study that is not a survey. 3. Determine the best method for producing data to answer a specific question: experiment, survey, or other observational study. 4. Locate available data on the Internet to help you answer a question of interest...
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...Business Solutions Private Limited, 2012 No part of this book should be referenced or copied without the prior permission of the company. A FEW WORDS TO THE STUDENTS Analytics is becoming a popular tool for managerial decision making. It‘s still not so widespread in countries like India, but in the west it has become a standard practice. Previously studying analytics involved an in depth knowledge of statistics and programming languages. But widespread availability of statistical package software has changed the reality to some extent. Now more emphasis is given on the application of the techniques to solve the business problems. So there is a need to understand the meaning of the statistical procedures. This book has been written to cater that need. In this book, all the necessary concepts have been explained keeping the business problem in mind. Also, to remove the apathy for statistics, use of mathematical expressions have been limited. That doesn‘t imply that we don‘t have to study the mathematics part. The intention is to put the substance over matter. As the students get accustomed to these statistical concepts, they can go for further investigations using various mathematical and statistical techniques. A list of suggested books and links have been given in the appendix. This book is directly related to the instructor‘s presentation. So it is highly advised that students should go through this material at the end of each class. As for general reading, the...
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...Newsvendor Model Chapter 11 1 utdallas.edu/~metin Learning Goals Determine the optimal level of product availability – Demand forecasting – Profit maximization Service measures such as a fill rate utdallas.edu/~metin 2 Motivation Determining optimal levels (purchase orders) – Single order (purchase) in a season – Short lifecycle items 1 month: Printed Calendars, Rediform 6 months: Seasonal Camera, Panasonic 18 months, Cell phone, Nokia Motivating Newspaper Article for toy manufacturer Mattel Mattel [who introduced Barbie in 1959 and run a stock out for several years then on] was hurt last year by inventory cutbacks at Toys “R” Us, and officials are also eager to avoid a repeat of the 1998 Thanksgiving weekend. Mattel had expected to ship a lot of merchandise after the weekend, but retailers, wary of excess inventory, stopped ordering from Mattel. That led the company to report a $500 million sales shortfall in the last weeks of the year ... For the crucial holiday selling season this year, Mattel said it will require retailers to place their full orders before Thanksgiving. And, for the first time, the company will no longer take reorders in December, Ms. Barad said. This will enable Mattel to tailor production more closely to demand and avoid building inventory for orders that don't come. - Wall Street Journal, Feb. 18, 1999 utdallas.edu/~metin For tax (in accounting), option pricing (in finance)...
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...10, 2012 1 Contents Preface 4 Mathematics of Finance 1. Simple Interest . . . . . . . . . . . . . . . . . . . . . . . 2. Discrete and Continuous Compound Interest . . . . . . 3. Ordinay Annuity, Future Value and Sinking Fund . . . 4. Present Value of an Ordinay Annuity and Amortization . . . . Matrices and Systems of Linear Equations 5. Solving Linear Systems Using Augmented Matrices . . . . 6. Gauss-Jordan Elimination . . . . . . . . . . . . . . . . . . 7. The Algebra of Matrices . . . . . . . . . . . . . . . . . . 8. Inverse Matrices and their Applications to Linear Systems . . . . . . . . . . . . . . . . . . . . . . . . Linear Programming 9. Solving Systems of Linear Inequalities . . . . . . . . . . . . . . 10. Geometric Method for Solving Linear Programming Problems 11. Simplex Method for Solving Linear Programming Problems . 12. The Dual Problem: Minimization with ≥ Constraints . . . . . Counting Principles, Permuations, and 13. Sets . . . . . . . . . . . . . . . . . . 14. Counting Principles . . . . . . . . . 15. Permutations and Combinations . . . . . . 5 5 12 19 26 . . . . 34 34 42 53 62 . . . . 69 69 77 86 97 Combinations 106 . . . . . . . . . . . . . . . 106 . . . . . . . . . . . . . . . 117 . . . . . . . . . . . . . . . 123 Probability 129 16. Sample Spaces, Events, and Probability . . . . . . . . . . . . . 129 17. Probability of Unions and...
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...sier!™ ing Everything Ea Mak ta t i s t i c s S e nt ia l s Ess Learn: • Exactly what you need to know about statistical ideas and techniques • The “must-know” formulas and calculations • Core topics in quick, focused lessons Deborah Rumsey, PhD Auxiliary Professor and Statistics Education Specialist, The Ohio State University Statistics Essentials FOR DUMmIES ‰ by Deborah Rumsey, PhD Statistics Essentials For Dummies® Published by Wiley Publishing, Inc. 111 River St. Hoboken, NJ 07030-5774 www.wiley.com Copyright © 2010 by Wiley Publishing, Inc., Indianapolis, Indiana Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions. Trademarks: Wiley, the Wiley Publishing logo, For Dummies, the Dummies Man logo, A Reference for the Rest...
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...Probability & Statistics for Engineers & Scientists This page intentionally left blank Probability & Statistics for Engineers & Scientists NINTH EDITION Ronald E. Walpole Roanoke College Raymond H. Myers Virginia Tech Sharon L. Myers Radford University Keying Ye University of Texas at San Antonio Prentice Hall Editor in Chief: Deirdre Lynch Acquisitions Editor: Christopher Cummings Executive Content Editor: Christine O’Brien Associate Editor: Christina Lepre Senior Managing Editor: Karen Wernholm Senior Production Project Manager: Tracy Patruno Design Manager: Andrea Nix Cover Designer: Heather Scott Digital Assets Manager: Marianne Groth Associate Media Producer: Vicki Dreyfus Marketing Manager: Alex Gay Marketing Assistant: Kathleen DeChavez Senior Author Support/Technology Specialist: Joe Vetere Rights and Permissions Advisor: Michael Joyce Senior Manufacturing Buyer: Carol Melville Production Coordination: Lifland et al. Bookmakers Composition: Keying Ye Cover photo: Marjory Dressler/Dressler Photo-Graphics Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and Pearson was aware of a trademark claim, the designations have been printed in initial caps or all caps. Library of Congress Cataloging-in-Publication Data Probability & statistics for engineers & scientists/Ronald E. Walpole . . . [et al.] — 9th ed. p. cm. ISBN 978-0-321-62911-1...
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...Introduction The Sample Mean The Central Limit Theorem The Sample Variance Sampling Distribution from The Normal Distribution Sampling from A Finite Population ◦ Distribution of The Sample Mean ◦ Joint Distribution of X and S2 ◦ Approximate Distribution of The Sample Mean ◦ How Large A Sample Is Needed 2 1 10/24/2011 Recall definitions of: ◦ ◦ ◦ ◦ ◦ ◦ ◦ Population Sample Inferential statistics Sampling Random sampling Parameter Statistic 3 If X1, . . . , Xn are independent random variables having a common distribution F, g , then we say that they constitute a sample (sometimes called a random sample) from the distribution F. 4 2 10/24/2011 Parametric inference problem: Problems in which the form of the underlying distribution is specified up to a set of unknown parameters, eg: Nonparametric inference problem: problems in hi h i which nothing is assumed about the form thi i d b t th f of F ◦ F was assumed as a normal distribution function having an unknown mean and variance 5 µ: population mean, σ2:population variance Let X1, X2, . . . , Xn be a sample of values from this population. The sample mean is defined by 6 3 10/24/2011 X is also a random variable 7 X is also centered about the population mean μ, but its spread becomes more and more reduced as the sample size increases. 8 4 10/24/2011 9 ◦ Distribution of The Sample Mean 10 5 10/24/2011 Let X1, X2, . . . , Xn be a sequence...
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...1) What is the primary function or purpose of descriptive statistics? Summarize complex data in a useful and informative way Explanation: In other words, descriptive statistics is all about making sense of complex data. 2) What do we call the process of gathering, organizing, summarizing, analyzing, and interpreting data? Statistics Explanation: This is the most basic definition of statistics. 3) The performance of financial investments is measured with a percentage know as return on investment. What kind of variable do we call return on investment? Continuous Explanation: The variable amount is constantly changing with the financial environment, thus called continuous. 4) What kind of variable is the amount of burglaries reported in a particular city? Discrete Explanation: A discrete variable is only able to collect data from a finite number of values. Infinite values cannot be accepted. 5) Name the level of measurement of the total number of auto accidents reported in a certain month? Ratio Explanation: Measuring an exact point on the scale is considered the ratio level of measurement. 6) The titles of the job positions in a company, such as chief operating officer or CEO, are examples of what level of measurement? Nominal Explanation: The nominal scale differentiates between items or subjects based only on their names. 7) Sneaker sizes, such as 6A, 11D, and 14FF, would be considered which level of measurement...
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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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...A FIRST COURSE IN PROBABILITY This page intentionally left blank A FIRST COURSE IN PROBABILITY Eighth Edition Sheldon Ross University of Southern California Upper Saddle River, New Jersey 07458 Library of Congress Cataloging-in-Publication Data Ross, Sheldon M. A first course in probability / Sheldon Ross. — 8th ed. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-13-603313-4 ISBN-10: 0-13-603313-X 1. Probabilities—Textbooks. I. Title. QA273.R83 2010 519.2—dc22 2008033720 Editor in Chief, Mathematics and Statistics: Deirdre Lynch Senior Project Editor: Rachel S. Reeve Assistant Editor: Christina Lepre Editorial Assistant: Dana Jones Project Manager: Robert S. Merenoff Associate Managing Editor: Bayani Mendoza de Leon Senior Managing Editor: Linda Mihatov Behrens Senior Operations Supervisor: Diane Peirano Marketing Assistant: Kathleen DeChavez Creative Director: Jayne Conte Art Director/Designer: Bruce Kenselaar AV Project Manager: Thomas Benfatti Compositor: Integra Software Services Pvt. Ltd, Pondicherry, India Cover Image Credit: Getty Images, Inc. © 2010, 2006, 2002, 1998, 1994, 1988, 1984, 1976 by Pearson Education, Inc., Pearson Prentice Hall Pearson Education, Inc. Upper Saddle River, NJ 07458 All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher. Pearson Prentice Hall™ is a trademark of Pearson Education, Inc...
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...circumstance”……………………………………...Bowley. STRUCTURE: 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 Introduction Meaning and Definitions of Statistics Types of Data and Data Sources Types of Statistics Scope of Statistics Importance of Statistics in Business Limitations of statistics Summary Self-Test Questions Suggested Readings 1.1 INTRODUCTION For a layman, ‘Statistics’ means numerical information expressed in quantitative terms. This information may relate to objects, subjects, activities, phenomena, or regions of space. As a matter of fact, data have no limits as to their reference, coverage, and scope. At the macro level, these are data on gross national product and shares of agriculture, manufacturing, and services in GDP (Gross Domestic Product). 1 At the micro level, individual firms, howsoever small or large, produce extensive statistics on their operations. The annual reports of companies contain variety of data on sales, production, expenditure, inventories, capital employed, and other activities. These data are often field data, collected by employing scientific survey techniques. Unless regularly updated, such data are the product of a one-time effort and have limited use beyond the situation that may have called for their collection. A student knows statistics more intimately as a subject of study like economics, mathematics, chemistry, physics, and others. It is a discipline, which scientifically deals with data,...
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