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Unformatted text preview: Cov ( X,Y ) = E [( X-E X )( Y-E 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 [(( X-E X ) + ( Y-E Y )) 2 ] = E [( X-E X ) 2 + 2( X-E X )( Y-E Y ) + ( Y-E 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