Skewness‚ Kurtosis‚ and the Normal Curve Skewness In everyday language‚ the terms “skewed” and “askew” are used to refer to something that is out of line or distorted on one side. When referring to the shape of frequency or probability distributions‚ “skewness” refers to asymmetry of the distribution. A distribution with an asymmetric tail extending out to the right is referred to as “positively skewed” or “skewed to the right‚” while a distribution with an asymmetric tail extending out to
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weights to the observations we can set s i 1 i u m 2 n 2 n i where m i 1 i 1 5 ARCH(m) Model AutoRegressive Conditional Heteroskedasticity In an ARCH(m) model we also assign some weight to the long-run variance rate‚ VL: s VL i 1 i u m 2 n 2 n i where m i 1 i 1 6 ARCH(m) Model AutoRegressive Conditional Heteroskedasticity Robert Fry Engle is an American economist and the winner of the 2003 Nobel Memorial
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DC-1 Sem-II Chapter: Covariance and Correlation Content Developers: Vaishali Kapoor & Rakhi Arora College / University: Rajdhani College (University of Delhi) Institute of Lifelong Learning‚ University of Delhi 1 Table of Contents 1. Learning outcomes 2. Introduction 3. Covariance a. Discrete Random Variable b. Continuous Random Variable c. Special cases 4. Correlation 5. Appendix 6. Summary 7. Exercises 8. Glossary 9. References Institute of Lifelong Learning‚ University
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be drawn from normally distributed populations. • These populations should have equal variances. • The measurement scales should be at least interval so that arithmetic operations can be used with them. Parametric tests place different emphasis on the importance of assumptions. Some tests are quite robust and hold up well despite violations. For others‚ a departure from linearity or equality of variance may threaten the validity of the results. Assessing the consequences of violating a statistical
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Practice Quiz I 1. The following bar chart describes the results of a survey concerning the relevance of study to present job by school. Focus on the School of Business and Management. What are the mode and the median respectively? (a) Relevant‚ Neutral (b) Relevant‚ Relevant (c) Neutral‚ Relevant (d) Neutral‚ Neutral 2. Some graphical descriptions of final examination scores for students of a Statistics course are given below. Please indicate which one is false. (a) (b) (c)
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Contents Univariate Data 2 Central tendency 2 Mean 2 Median 3 Mode 3 Trimean 3 Trimmed Mean 3 Spread 3 Range 3 Semi Inter Quartile Rang 3 Variance and Standard Deviation 3 Skew 3 Graphical Representations 4 Frequency Polygons& Cumulative Frequency Polygons 4 Histograms & Bar Graphs 4 Stem and Leaf plots 4 Box Plots 4 Describing Bivariate Data 4 Scatterplots 4 Pearson’s Correlation 4 Spearman’s Rho 4 Probability 4 Binomial Distribution 4 Assumptions:
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Version 1 FINANCE 261 FINANCE 261 Test Answer Sheet Name: __________________________________________ Student ID Number:_______________________________ Please use CAPITAL LETTERS when writing your answers. Question Answer Question Answer Question Answer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Question Answer 16 17 18 19 20 1 Version 1 FINANCE 261 THE UNIVERSITY OF AUCKLAND Department of Accounting and Finance FINANCE
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Gauss Markov Theorem In the mode [pic]is such that the following two conditions on the random vector [pic]are met: 1. [pic] 2. [pic] the best (minimum variance) linear (linear functions of the [pic]) unbiased estimator of [pic]is given by least squares estimator; that is‚ [pic]is the best linear unbiased estimator (BLUE) of [pic]. Proof: Let [pic]be any [pic]constant matrix and let [pic]; [pic] is a general linear function of [pic]‚ which we shall take as an estimator of [pic]. We must specify
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by the “LESS THAN OGIVE” graph. Mean Pocket Money of Students ( Computation of Sample Mean from Grouped Data) Mean( x’)= Summation(fiMi) / n = 3967.17 Sample Variance of Pocket Money received by IFIM Students: Sample Variance s2 = Summation (fi(Mi – x’)2) / n – 1 = 55466666.7 / 30 – 1 = 1912643.68 Stating the variance gives an impression of how closely concentrated round the expected value the distribution is; it is a measure of the ’spread’ of a distribution about its average value
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II. STATEMENT OF THE PROBLEM As part of a long-term study of individuals 65 years of age or older‚ sociologists and physicians at the Wentworth Medical Center in upstate New York investigated the relationship between geographic location‚ health status ( healthy or one or more comorbidities)‚ and depression. Random samples of 20 healthy individuals were selected from three geographic locations: Florida‚ New York‚ and North Carolina. Then‚ each was given a standardized test to measure depression
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