Convert Monthly to Annual Returns and Standard Deviations: Annual Mean Return: RA=12*RM Annual Standard Deviation: STDEVA= 12* VarM= 12*STDEVM 4. Portfolio (equally weighted): Monthly Return: RP= iwiRi equally weighted: RP= 110iRi → AVERAGE Variance: VarP= ijwiwjCovi‚j equally weighted: VarP= (110)2ijCovi‚j Covariance Matrix: Cov1‚1⋯Cov1‚n⋮⋱⋮Covn‚1⋯Covn‚n → symmetric Create Covariance Matrix: Two Options: 1. Data Analysis (Add-In Tool) (indirectly‚ returns population covariance)
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RISK THEORY - LECTURE NOTES 1. INTRODUCTION The primary subject of Risk Theory is the development and study of mathematical and statistical models to describe and predict the behaviour of insurance portfolios‚ which are simply financial instruments composed of a (possibly quite large) number of individual policies. For the purposes of this course‚ we will define a policy as a random (or stochastic) process generating a deterministic income in the form of periodic premiums‚ and incurring financial
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ETF2121/ETF5912 Data Analysis in Business Unit Information – Semester 1 2014 Coordinator and Lecturer - Weeks 7-12: Associate Professor Ann Maharaj Office: H5.86 Phone: (990)32236 Email: ann.maharaj@monash.edu Lecturer - Weeks 1-6: Mr Bruce Stephens Office: H5.64 Phone: (990)32062 Email: bruce.stephens@monash.edu Unit material: No prescribed textbook Unit Book: available on the Moodle site. Exercises: available on the Moodle site. Software: EXCEL. Recommended Reference Books Berenson
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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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York‚ and 20 were residents of North Carolina. From the data collected we could know that the higher test scores indicate higher levels of depression. The descriptive statistics of the data collected are as following: GROUPS SIZE SUM MEAN SAMPLE VARIANCE FLORIDA 20 88.50 4.42 3.81 NEW YORK 20 131.53 6.58 3.95 NORTH CAROLINA 20 137.09 6.85 2.31 For the second part of this study‚ we considered the relationship between geographic location and depression for individuals 65 years of age or older
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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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variability explained by the fitted value is relatively high with 96.23%. This means that transformed data in blood flow explains 96.23% of the variation in the transformed data in arterial oxygen. 4. Check the normality of residuals and equal variances predict r‚ resid kdensity r‚ normal pnorm tx qnorm tx rvpplot tx Before we could perform the numerical test‚ we must first generate the r by the command “predict r‚ resid” swilk r 5. Check the homoscedasticity of the residuals
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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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: Time Series‚ Cross Section and Panel Data. Concept of PRF and SRF. Estimation of the SRF using OLS. Analysis of variance and R squared. Understanding the residuals/error term. Assumptions of the model. Expectation and standard errors of the regression coefficients and the error term. Gauss Markov Theorem. Confidence intervals and tests on population regression coefficients‚ variance of population disturbance term‚ and forecasts. Testing the significance of the model as a whole. Testing the normality
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observations‚ which measure of central tendency reports the value that occurs most often? A. Mean B. MedianC. ModeD. Geometric mean 4) Which level of measurement is required for the median? A. Nominal B. OrdinalC. IntervalD. Ratio 5) The mean and the variance are equal in…A. the normal distributionB. the binomial distributionC. the Poisson distributionD. the hypergeometric distribution 6) The difference between the sample mean and the population mean is called the…A. margin of errorB. population standard
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