例2设X~P(a求D(X) 解°x的概率函数为 P{X=}= 2 e k=0,1,2,…,>0 ! E(X)=而E(X)之在x2 =∑[k(k-1)+k a e =0 ! k e 2e ∑k(k-1) +∑k e + (k-2) k=0 ! k=0 ! 2ee2+=2+aD(X)=E(X2)-E(X)2=元 因此,泊松分布E(X)=元,D(X)=元例2 设X ~ P()，求D(X)。 解 X的概率函数为 , 0,1,2, , 0 ! { = } = =  −    k  k e P X k k E(X) = ,而 ( ) = 2 E X   = − 0 2 ! k k k e k     = − − − = 2 2 2 ( 2)! k k k e          = + = + 2 − 2 e e    =  − = − = − + 0 0 ! ! ( 1) k k k k k e k k e k k     = − =  2 2 D(X) E(X ) [E(X)] 因此,泊松分布 E(X) = ,D(X) =  +    = − = − + 0 ! [ ( 1) ] k k k e k k k  