ch6-53 证1设x(m)=∑2X,~N01)1=12,…,n X.X Xn相互独立, 则E(X)=0,DX)=1,E(X2)=1 n 2()=∑x|=n E(X)=t] 2dx=3 2兀 D(X2)=E(K4)-E2(X2)=2 D(2(o)=D∑x2|=2nch6 -53 X X Xn , , , 1 2  相互独立 , 证 1  设 = = = ni i i n X X N i n 1 2 2  ( ) ~ (0,1) 1,2,, 则 ( ) 0, ( ) 1, ( ) 1 2 = = = E Xi D Xi E Xi E( n ) E X n ni i  =  = =1 2 2  ( ) d 3 21 ( ) 22 4 4 = = − − E X x e x x i  ( ) ( ) ( ) 2 2 4 2 2 D Xi = E Xi − E Xi = D( n ) D X n ni i ( ) 2 1 2 2  =  = = 