证明:E(Xx)=mp。 证E(x)=2mCmp"(-pym ∑m n p"(-p) n-m n n' p (m-1)|(-1-(m- (1-p)"m p·∑cm1p-(1-p)"m m-1=0 nplp+(1-p) -1 np 类似地可得:Ex2=m-1y2+m, 于是方差DX=EX2-(EX)2 npq证明： E( ) X = np 。 [证] E( ) X = m n m n m m n m C p p − = ∑ ⋅ (1− ) 0 m n m n m p p m n m n m − = ⋅ − ⋅ − = ∑ ⋅ (1 ) !( )! ! m=0 m!(n m)! 0 1 ( 1) ( 1) (1 ) ( 1)![( 1) ( 1)]! ( 1)! − − − − − − − − − − = ⋅ ⋅∑ m n m n p p m n m n n p 1 ( 1)![( 1) ( 1)]! m= m− n− − m− ∑ − − − − − − = ⋅ − − 1 1 1 ( 1) ( 1) 1 (1 ) n m m n m np Cn p p = +− − np p p n [ ( )] 1 1 = np ∑ m−1=0 类似地可得： EX = n n − p + np 2 2 ( 1) ， 于是方差 DX EX EX 2 2 于是方差 DX = EX − (EX ) = npq 2 2 ( )