概车纶与款理统外 (2)利用公式计算 D(X)=E(X2)-E(X)P. 证明D(X)=E{X-E(X)) =E{X2-2XE(X)+[E(X)2} =E(X2)-2E(X)E(X)+[E(X)I2 =E(X2)-[E(X)2 =E(X2)-E2(X).( ) ( ) [ ( )] . 2 2 D X = E X − E X 证明 ( ) {[ ( )] } 2 D X = E X − E X { 2 ( ) [ ( )] } 2 2 = E X − XE X + E X 2 2 = E(X ) − 2E(X)E(X) + [E(X)] 2 2 = E(X ) − [E(X)] (2) 利用公式计算 ( ) ( ). 2 2 = E X − E X