例1设总体X服从[u,b上的均匀分布,a,b未知, X 1412,· X为来自总体X的样本,试求a,b的 矩估计量 解|1=EX)=2 a+6 H2se(x2)=D(X)+E(R(b-a)2(a+6)2 12 由矩估计法,令 a+b X-∑(Xx-x), n i=1 (b-a)2,(a+b) 44B=F+/33 ∑ X.-X 2 12 n i=1例1 设总体X服从[a,b]上的均匀分布,a,b未知, X1 , X2 , …,Xn为来自总体X的样本,试求a,b的 矩估计量. + + − = = + = + = = 4 ( ) 1 2 ( ) ( ) ( ) [ ( )] , 2 ( ) 2 2 2 2 2 1 b a a b E X D X E X a b E X 解 由矩估计法,令 = + + − = + 2 2 2 1 4 ( ) 12 ( ) 2 A b a a b A a b = + − = − − 3( ) ˆ ˆ 3( ) 2 1 2 1 2 1 2 1 b A A A a A A A = = = + − = − − n i i n i i X X n b X X X n a X 1 2 1 2 ( ) 3 ˆ ( ) , 3 ˆ