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Unformatted text preview: Cov ( X,Y ) = E [( XE X )( YE Y )] . As with the variance, Cov ( X,Y ) = E ( XY )( E X )( E Y ). It follows that if X and Y are independent, then E ( XY ) = ( E X )( E Y ), and then Cov ( X,Y ) = 0. Note Var ( X + Y ) = E [(( X + Y )E ( X + Y )) 2 ] = E [(( XE X ) + ( YE Y )) 2 ] = E [( XE X ) 2 + 2( XE X )( YE Y ) + ( YE Y ) 2 ] = Var X + 2Cov ( X,Y ) + Var Y. We have the following corollary. 23...
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This note was uploaded on 12/29/2011 for the course MATH 317 taught by Professor Wen during the Spring '09 term at SUNY Stony Brook.
 Spring '09
 wen

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