概车纶与款理统外 (3)设X,Y相互独立，D),D()存在，则 D(X±Y)=D(X)+D(Y): 证明 D(X±Y)=EI(X±Y)-E(X±Y)I} =EX-E(X)】±Y-E(Y)}2 EIX-E(X)2+E[Y-E(Y) ±2E{[X-E(X)川Y-E(Y)} =D(X)+D(Y).D(X  Y ) = D(X) + D(Y ). (3) 设 X, Y 相互独立, D(X), D(Y) 存在, 则 证明 ( ) {[( ) ( )] } 2 D X  Y = E X  Y − E X  Y 2 = E{[X − E(X)] [Y − E(Y )]} 2 {[ ( )][ ( )]} [ ( )] [ ( )] 2 2 E X E X Y E Y E X E X E Y E Y  − − = − + − = D(X) + D(Y )