Unformatted text preview: E ( XY ) = ( E X )( E Y ) . Proof. By the above with g ( x,y ) = h ( x ) k ( y ), E [ h ( X ) k ( Y )] = Z Z h ( x ) k ( y ) f ( x,y ) dxdy = Z Z h ( x ) k ( y ) f X ( x ) f Y ( y ) dxdy = Z h ( x ) f X ( x ) Z k ( y ) f Y ( y ) dy dx = Z h ( x ) f X ( x )( E k ( Y )) dx = E h ( X ) E k ( Y ) . 39...
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This note was uploaded on 12/29/2011 for the course MATH 316 taught by Professor Ansan during the Spring '10 term at SUNY Stony Brook.
 Spring '10
 ansan

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