E(x2)=∑12p ∑(-1)p+∑ ∑(i-1) pq(2q)+(3q2)+…+(iq-)y+…)+ pq(q+q+…+q+…)"+ q(1-q)+ (1-q) (2-2q1-q)2-(2q-q2)·2(1-q(-1) y2(-q)2+(1-g2)21 2 ∴D(X)=E(x2)-[E(X q+p q x 泊松分布:P(X=D=P=e,=0,1,2 E(X)=元 E(X2)=∑2·p ∑(-D,e-+∑,e2 3 3 2 2 4 2 2 2 2 2 2 2 2 3 2 1 2 1 1 1 1 2 2 2 1 (1 ) 2 1 (1 ) 2(1 ) (2 ) 2 1 (1 ) (2 2 )(1 ) (2 ) 2(1 )( 1) 1 (1 ) 2 1 (1 ) 2 (1 ) 1 1 1 ( ) 1 ((2 )' (3 )' ( )' ) 1 ( 1) ( 1) ( ) p q p q p pq q p q q q pq q p q q q q q pq q p q q pq q p q q q pq q p q pq p pq q q q p pq q q iq p i i pq i i p ip E X i p i i i i i i i i i i + = + − = + − − + −  = + − − − − −  − − = +        − − = +        − − + = +        − = = + + + +  + = + + + + + = −  + = − + =  −  = −  =  =  =         ∴ 2 2 D(X) = E(X ) −[E(X)] 泊松分布：    = = = = = − , 0, 1, 2, ( ) ! ( ) e i E X i P X i p i i    = =  0 2 2 ( ) i pi E X i 2 2 2 2 1 p q p p q p = − + =    =  = − − = −  +  1 1 ! ! ( 1) i i i i e i e i i i i    