distribution of ηt+1 . With time-varying σt ‚ the unconditional distribution of ηt+1 has fatter tails than a normal distribution. To show this define ηt+1 as follows: ηt+1 = σt 4 t+1 (3) where t+1 is IID with zero mean and unit variance. A useful measure of tail thickness is the fourth moment or kurtosis‚ i.e.‚ K(y) = E[y 4 ]/E[y 2 ]2 . It is well known that the kurtosis of a normal random variable is 3; hence K( t+1 ) 4 = E[ ( t+1 −µ) ] = E[ 4 ] = 3. When considering the innovations of
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University of Phoenix Material Week Four Quiz 1. WHICH OF THE FOLLOWING STATEMENTS ARE CORRECT? a. A normal distribution is any distribution that is not unusual. (Correct) b. The graph of a normal distribution is bell-shaped. (Correct) c. If a population has a normal distribution‚ the mean and the median are not equal. d. The graph of a normal distribution is symmetric. (Correct) Using the 68-95-99.7 rule: Assume that a set of test scores is normally distributed
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Table of Contents Introduction Cricket involves numbers‚ the comparison of these numbers will give us an idea regarding how well a team is faring. The comparison of these number widely depends on Statistics to give us a rational conclusion. Cricket is therefore a sport which involves a lot of statistics‚ Statistics are needed to determine the performance of a team in various formats such as one day‚ international. It is also needed to determine the performance
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____ 1. The pie chart describes the distribution of state tree types for the 50 states in the United States. The category “Other” include all trees that are the state tree for two or fewer states. Which of the following conclusions can we draw from this chart? a. Some states have not designated a “state tree.” b. The cottonwood is the state tree for 12 states. c. Taken together‚ oak‚ pine‚ and maple are the state trees for more than half the states. d. There are 10 states that have designated
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selling the house within 7 weeks (49 days)‚ first compute Z 49 mean / std.dev. 49 46 / 7.0789 0.4238 Looking this z-value up in the standard-normal table results in a probability of 0.664 for selling the house within 7 weeks. Question 2 (e) To determine this value‚ first find a z-value in the standard-normal table such that the area to the left is 0.95. That z-value is 1.645. Then‚ the
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potential threat coming towards them. But during the night‚ they cannot see‚ so they huddle close together to stay safe. B) If I were to design a controlled experiment‚ I would take two samples. one in which the Bursatella leachii was placed in its normal environment. The second sample would have the Bursatella leachii in a controlled environment‚ where we could control the brightness‚ darkness‚ and the temperature of the water. Since we know what would happen if the Bursatella leachii are in contact
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1) Write the following as an algebraic expression using x as the variable: Twelve less than six times a number A. 6x – 12 [(Six times a number means 6x‚ and twelve less mean -12)] B. –6x C. –12(6x) D. 12 – 6x 2) Write the following as an algebraic expression using x as the variable: The sum of a number and -8 A. -8 + x [(let x be the variable number‚ therefore sum of variable (x) and (-8) would be x-8 or -8 + x)] B. -8 - x C. x(-8) D. -8x 3) Write the following as
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MATHEMATICS GCE Advanced Subsidiary and GCE Advanced Level 9709 CONTENTS Page INTRODUCTION 1 AIMS 2 ASSESSMENT OBJECTIVES 2 ASSESSMENT 3 CURRICULUM CONTENT 5 RESOURCE LIST 16 LIST OF FORMULAE AND TABLES OF THE NORMAL DISTRIBUTION 18 MATHEMATICAL NOTATION 23 MATHEMATICS 9709 (2009) INTRODUCTION The syllabus has been designed to allow Centres flexibility to construct Mathematics courses appropriate to their candidates‚ in terms of both the content
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Norte State College‚ New Visayas‚ Panabo City picar_joy@yahoo.com ABSTRACT The efficiency of Mean Square Error (MSE) of the random normal variables generated from both the Marsaglia Polar Method and Box-Muller Method was examined for small and large n with Monte-Carlo application using MATHLAB. The empirical results showed that MSE of the random normal variables using the Marsaglia Polar Method approaches zero as n becomes larger. Moreover‚ when run in MATHLAB‚ the Box-Muller method
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STA2300 Data Analysis Faculty of Sciences Study Book Ashley Plank with contributions from The LTS Team‚ Christine McDonald‚ Paul Fahey‚ Peter Dunn‚ Shahjahan Khan‚ Taryn Swan & Rachel King ii c University of Southern Queensland‚ 2012.1 Published by University of Southern Queensland Toowoomba Qld 4350 Australia http://www.usq.edu.au Copyrighted materials reproduced herein are used under the provisions of the Copyright Act 1968 as amended‚ or as a result of application to the copyright
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