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WORKED EXAMPLES 3 COVARIANCE CALCULATIONS

Hence the two variables have covariance and correlation zero But note that Xand Y are not inde-pendent as it is not true that f X,Y(x,y) = f X(x)f Y(y) for all xand y 2



Covariance Covariance Matrix

Covariance • Variance and Covariance are a measure of the “spread” of a set of points around their center of mass (mean) • Variance – measure of the deviation from the mean for points in one dimension e g heights • Covariance as a measure of how much each of the dimensions vary from the mean with respect to each other



Covariance & Correlation - UNIGE

Covariance & Correlation The covariance between two variables is defined by: cov x,y = x x y y = xy x y This is the most useful thing they never tell you in most lab courses Note that cov(x,x)=V(x) The correlation coefficient is a unitless version of the same thing: = cov x,y x y If x and y are independent variables (P(x,y) = P(x)P(y)), then



Covariance Matrices - Stanford University

Oct 29, 2009 · Identities For cov(X) – the covariance matrix of X with itself, the following are true: cov(X) is a symmetric nxn matrix with the variance of X i on the diagonal cov cov





Chapter 5: JOINT PROBABILITY DISTRIBUTIONS Part 2: Covariance

Covariance is a measure of the linear relationship between two variables, but perhaps a more com-mon and more easily interpretable measure is correlation Correlation The correlation (or correlation coe cient) be-tween random variables Xand Y, denoted as ˆXY, is ˆXY = cov(X;Y) p V(X)V(Y) = ˙XY ˙X˙Y Notice that the numerator is the covariance,



Variance, covariance, correlation, moment-generating functions

Variance, covariance, correlation, moment-generating functions [In the Ross text, this is covered in Sections 7 4 and 7 7 See also the Chapter Summary on pp 405–407 ]



TI BA II Plus Calculator Functions

Sample Covariance Year Stock 1 Stock 2 1 +0 05 +0 07 2 –0 02 –0 04 3 +0 12 +0 18 Example: Calculate the covariance between the return on the two stocks indicated



THÉORIE DE PORTEFEUILLE

a Calcul de la covariance entre les rendements de deux titres i et j à partir du probabilités subjectives Avec : Rik: Rendement du titre i étant donné la conjoncture k ; Rik: Rendement du titre j étant donné la conjoncture k ; Pk: Probabilité de réalisation de la conjoncture k II - MESURE DE RISQUE i j 1 i1 i j1 j

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