)-t-jg'a-t+6+6 b-a D(X)=E(X)-[E(X)P(6-a) 12 例4设X服从参数为1的指数分布，求 D(X). 解 0X2)=r1xtr==是， D)=Er)-iEXP=是 例5设X~N(4,o2),求 D(X). 解f)=1e e2a,-0<X<+o0, E()=u. √2π0. 12 ( ) ( ) ( ) [ ( )] , 3 d 1 ( ) ( )d 2 2 2 2 2 2 2 2 b a D X E X E X a a b b x b a E X x f x x x b a − = − = + + = − = =   + − 例4 设 X 服从参数为 的指数分布，求 D( X )．       = − 0, 0 e , 0 ( ) x x f x x   1 E(X) = . 1 ( ) ( ) [ ( )] , 2 ( ) ( )d e d 2 2 2 2 0 2 2 2     = − = = = =   + − + − D X E X E X E X x f x x x x x 解 ， ． 例5 设 ，求 D( X ) ． ~ ( , ) 2 X N   = −    + − − f x x x e , 2 1 ( ) 2 2 2 ( )    解 , . E(X ) = 