jxn
这道题我想了很多天,还没想出来,请大家帮忙看看,谢谢了
x1,x2,...xn,independent sequence of uniform random variables on interval(a,b),
suppose zeta=E(xi)=(a+b)/2 we wish to estimate.
let S=1/n*(x1+....xn), is a candidate estimate.
i) find the minimal sufficient statisitcs T for a and b
ii) find S* by using T (Rao-Blackwell improvement of S)
我找出了T={x(1), x(n)}, 准备用Rao-Blackwellization,
S*=E(S|T)=E(1/n*(x1+....xn)|(x(1),x(n)))
这个条件期望E(1/n*(x1+....xn)|(x(1),x(n)))怎么算呢?条件是(x(1),x(n)),不会展开,