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Unformatted text preview: âˆ« âˆ« âˆ« Derivation of the third property of covariance (p.4/6): ( 29 [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] Y Var b Y X abCov X Var a b ab a Y E b XY abE X E a b a Y b abXY X a E bY aX E bY aX E bY aX Var y y x x y x 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 , 2 2 2 2 ] [ + + =+ + = ++ + = ++ = + Î¼ Example of linear operations on Variance of binomial: Let X ~ Binomial Then: [ ] [ ] âˆ‘ = i X Var X Var where each X i is distributed according to Bernouilli distribution [ ] ( 29 [ ] [ ] ( 29 p np X Var n X Var p p X Var i i i= â‹… == âˆ‘ 1 1 Thus, the known variance of the binomial distribution np(1p) results....
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 '08
 Stedinger
 Normal Distribution, Variance, Probability theory, 1w, Bernouilli distribution, xy dxdy xy

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