例3设X~B(n,p),求E(X). 解X的分布律为 p%=P{X=k=Cp(1-p)"-,k=0,1,2,…,n F0=空奶rI-p k=0 =np>Cp-(1-p)(-D-(-D k=1 =np(p+1-p)" =np. 例4设X~π(2)，求E(X)· 解Pk=P{X=}= e,k=0,1,2,… k例3 设 X ~ B(n, p) ，求 E(X ) ． . ( 1 ) (1 ) (1 ) !( )! ! ( ) { } (1 ) , 0,1, 2, , 1 1 1 1 ( 1) ( 1) 1 0 1 n p n p p p n p C p p p p k n k n E X k p k p P X k C p p k n n n k k k n k n n k k n k n k k k k n k k n = = + − = − − − = = = = = − = − = − − − − − − = − = −     解 X 的分布律为 例4 设 X ~ () ，求 E(X ) ． , 0, 1, 2, ! = { = } = = − e k k p P X k k k   解