证1°设x2()）=∑X好X,N(0,)i=1,2,…,n i1 X1,X2,…,X,n相互独立， E(X)=0,D(X)=1,E(X)=1 则 -42x好=n D(X)=E(X4)-E2(X2)=2 ()2n X X Xn , , , 1 2  相互独立, 证 1° 设 ∑= = = n i i i n X X N i n 1 2 2 χ ( ) ~ (0,1) 1,2,, 则 ( ) 0, ( ) 1, ( ) 1 2 = = = E Xi D Xi E Xi E( n ) E X n n i i  =      = ∑=1 2 2 χ ( ) d 3 2 1 ( ) 2 2 4 4 = = ∫ ∞ −∞ − E X x e x x i π ( ) ( ) ( ) 2 2 4 2 2 D Xi = E Xi − E Xi = D( n ) D X n n i i ( ) 2 1 2 2  =      = ∑= χ