cov x y e xy e x e y Cov X Y E X X Y Y Notice that the variance of Xis just the covariance of Xwith itself Var X E X X 2 Cov X X Analogous to the identity for variance Var X E X2 2 X
One of the applications of covariance is finding the variance of a sum of several random variables In particular if Z X Y then Var Z Cov Z Z Cov X Y X Y E XY E X E Y E g X h Y E g X E h Y Notes 1 E XY E X E Y is ONLY generally true if X and Y are INDEPENDENT 2 If X and Y are independent then E XY
cov x y e xy e x e y
cov x y e xy e x e y
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Solved 3 We Know That Cov X Y E X E X Y E Y Use Chegg
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Solved 1 Let cov X Y E XY E x E Y Denote The Chegg
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Using Cov X Y E XY E X E Y as a de nition certain facts are immediate Cov X Y Cov Y X Cov X X Var X Cov aX Y aCov X Y Cov X 1 E g X X x X g x f x where f is the probability mass function of X and X is the support of X 2 If X is continuous then the expectation of g X is de ned as E g X Z
The covariance of X and Y is Cov X Y E X E X Y E Y E XY E X E Y Note Covariance can be negative unlike variance This should remind you of the de nition of E X1 X1 E X2 X2 var X1 2 X1 var X2 2 X2 Also we assume that 2 X1 and 2 X2 are nite positive values A simpli ed notation 1 2 2 1 2 2 will be used
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Solved Prove That Cov X Y E XY E X E Y Given That Chegg
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Exponential Properties YouTube
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Portfolio Risk Analysis In SQL
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The covariance between two variables X and Y Cov X Y can be calculated by taking the expected value or mean E of the product of two values the Cov X Y E X E X Y E Y E XY E X E Y this is a generalization of variance to two random variables and generally measures the degree to which X and Y tend to be large
Cov X Y EXY X Y Theorem 4 5 5 If X and Y are independent random variables then Cov X Y 0 and XY 0 Theorem 4 5 6 If X and Y are any two random Covariance like variance can also written a different way Write x E X and Y E Y If laws of X and Y are known then X and Y are just constants Then Cov X Y
Lecture 15 1 Expectations 2 Covariance And Correlation
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Solved Definition The Covariance Between X And Y Is Cor X Chegg
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cov x y e xy e x e y - Using Cov X Y E XY E X E Y as a de nition certain facts are immediate Cov X Y Cov Y X Cov X X Var X Cov aX Y aCov X Y Cov X 1