Formula_sheet_bivnor

# Formula_sheet_bivnor - E Y | X = x = μ Y ρ σ Y σ X x-μ...

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OR 3500/5500, Fall’10 Formula sheet Formulas related to Bivariate Normal Distribution If ( X,Y ) is bivariate normal with parameters ( μ X Y X Y ), then its density is given by f X,Y ( x,y ) = 1 2 πσ X σ Y p (1 - ρ 2 ) exp - ( x - μ X ) 2 σ 2 X + ( y - μ Y ) 2 σ 2 Y - 2 ρ ( x - μ X )( y - μ Y ) σ X σ Y 2(1 - ρ 2 ) . Given X = x , the conditional distribution of Y has the following (condi- tional) mean and (conditional) variance:
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Unformatted text preview: E ( Y | X = x ) = μ Y + ρ σ Y σ X ( x-μ X ) , Var( Y | X = x ) = σ 2 Y (1-ρ 2 ) . • Given Y = y , the conditional distribution of X has the following (condi-tional) mean and (conditional) variance: E ( X | Y = y ) = μ X + ρ σ X σ Y ( y-μ Y ) , Var( X | Y = y ) = σ 2 X (1-ρ 2 ) . 1...
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## This note was uploaded on 10/29/2011 for the course MATH 3310 at Cornell.

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