设总体X〜N(μ,1),-∞

题目

设总体X〜N(μ,1),-∞

答案

Eμ1=(1/5)Ex1+(3/10)Ex2+(1/2)Ex3
=(1/5)μ+(3/10)μ+(1/2)μ=μ
μ1是μ的无偏估计.
类似地,μ2,μ3都是μ的无偏估计.
Dμ1=(1/5)^2*Dx1+(3/10)^2*Dx2+(1/2)^2*Dx3
=(1/5)^2+(3/10)^2+(1/2)^2
=0.38.
Dμ2=(1/3)^2+(1/4)^2+(5/12)^2=50/144=0.347...
Dμ3=(1/3)^2+(1/6)^2+(1/2)^2=14/36=0.388...
Dμ2