on sample information such as tables‚ graph‚ the mean‚ median‚ mode and etc. c) A researcher will use the F distribution to make an inference on the ratio between two population variances. d) To construct a 90% confidence interval for u‚ if a small sample was selected randomly from normal population with unknown variance‚ the t distribution is used. e) The significance level a is the probability of rejecting the null hypothesis when it is false. f) Non-parametric test is used when the data are not
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| Basic math symbols Symbol | Symbol Name | Meaning / definition | Example | = | equals sign | equality | 5 = 2+3 | ≠ | not equal sign | inequality | 5 ≠ 4 | > | strict inequality | greater than | 5 > 4 | < | strict inequality | less than | 4 < 5 | ≥ | inequality | greater than or equal to | 5 ≥ 4 | ≤ | inequality | less than or equal to | 4 ≤ 5 | ( ) | parentheses | calculate expression inside first | 2 × (3+5) = 16 | [ ] | brackets | calculate expression inside first
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1 Factor Models The Markowitz mean-variance framework requires having access to many parameters: If there are n risky assets‚ with rates of return ri ‚ i = 1‚ 2‚ . . . ‚ n‚ then we must know 2 all the n means (ri )‚ n variances (σi ) and n(n − 1)/2 covariances (σij ) for a total of 2n + n(n − 1)/2 parameters. If for example n = 100 we would need 4750 parameters‚ and if n = 1000 we would need 501‚ 500 parameters! At best we could try to estimate these‚ but how? In fact‚ it is easy to see
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ECON10005 QUANTITATIVE METHODS 1 Assignment 2 Semester 1‚ 2013 This assignment has four questions‚ and is due by 5.00pm on Thursday 2 May. It is to be submitted electronically as a .pdf file using the assignment tool on the subject’s LMS page. Marks depend on your tutor being able to understand your statements and arguments‚ so marks may be deducted for poor presentation or unclear language. Use nothing smaller than 12 point font. If you wish to write your assignment by hand and scan the file into
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remove anything +/- 20% 3. Calculate historical average and historical risk X-BAR = Σx/n Calculate the sum of the total return and divide by the number of observations • Variance = σ2 = Σ(x – x bar) 2 / (n-1) Fix X-BAR‚ double click to apply to all dates‚ get the sum‚ divide by (n-1) Risk = σ = √σ = SQRT(Variance) = standard deviation 4. Average Matrix Excel Options → Add-ins → Go → Select 1st two and last one → Go Data Analysis → Descriptive Analysis → Select all data without
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TORONTO Joseph L. Rotman School of Management RSM332 PROBLEM SET #2 SOLUTIONS 1. (a) Expected returns are: E[RA ] = 0.3 × 0.07 + 0.4 × 0.06 + 0.3 × (−0.08) = 0.021 = 2.1%‚ E[RB ] = 0.3 × 0.14 + 0.4 × (−0.04) + 0.3 × 0.08 = 0.05 = 5%. Variances are: 2 σA = 0.3 × (0.07)2 + 0.4 × (0.06)2 + 0.3 × (0.08)2 − (0.021)2 = 0.004389‚ 2 σB = 0.3 × (0.14)2 + 0.4 × (0.04)2 + 0.3 × (0.08)2 − (0.05)2 = 0.00594. Standard deviations are: √ 0.004389 = 6.625%‚ σA = √ 0.00594 = 7.707%. σB = Covariance
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(RA ‚ RB ) −0.0322 = = −1. σ (RA )σ (RB ) 0.14 × 0.23 The assets are perfectly negatively correlated. Consider portfolio P formed from assets A and B such that you invest α fraction of your wealth into A and (1 − α) fraction into B. The variance of such portfolio is σ (RP )2 = = = = α2 σ (RA )2 + (1 − α)2 σ (RB )2 + 2α(1 − α)Cov (RA ‚ RB ) α2 σ (RA )2 + (1 − α)2 σ (RB )2 + 2α(1 − α)σ (RA )σ (RB )ρ(RA ‚ RB ) α2 σ (RA )2 + (1 − α)2 σ (RB )2 − 2α(1 − α)σ (RA )σ (RB ) [ασ (RA ) − (1
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random variable X has the probability density function given by 3 2 ; 0 x2 (2 x) f ( x) 8 0 ; otherwise (i) Calculate the mean of X and variance of X. (ii) Calculate . (iii) Find . b) Given X ~ Exp ( 2) and the moment generating function (MGF) of X is given M X (t ) 2 2t . Find the mean and variance of X. c) Given for x = 1‚ 2‚ 3‚ 4. Find the moment generating function of X. Question 2 a) According to a survey‚ 45% of all students at a large university
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Theory of Errors and Least Squares Adjustment Huaan Fan ISBN 91-7170-200-8 Royal Institute of Technology (KTH) Division of Geodesy and Geoinformatics 100 44 Stockholm Sweden August 2010 Theory of Errors and Least Squares Adjustment Huaan Fan‚ PhD Royal Institute of Technology (KTH) Division of Geodesy and Geoinformatics Teknikringen 72‚ 100 44 Stockholm‚ Sweden Phone: +46 8 7907340 Fax: +46 8 7907343 E-mail: hfan@kth.se URL: http://www.infra.kth.se/impgg With 22 illustrations and 49
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Bivariate analysis Contingency table In this case‚ we use contingency table to analyze the relationship between 2 qualitative variables. And this test works by comparing expected and observed frequencies with x2 distribution. Correlation coefficient When we need to test the relationship between 2 quantitative variables‚ we use correlation coefficient and it measured by standardized covariance measure and investigates linear dependence. Before doing this‚ it is better to first make a scatterplot
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