One way is by using Cramer-Rao Lower Bound This will also tell you whether it is attained.
Let X1,X2,...,Xn be a random sample from a distribution with p.d.f.,
f(x;θ)=θ2xe^(−xθ);0<x<∞,θ>0
Obtain minimum variance unbiased estimator of θ and examine whether it is attained?
MY WORK:
Using MLE i have found the estimator for θ=2/(x bar)
Or as
X∼Gamma(2,θ)
So
E(X)=2θ
E(X/2)=θ
so can i take x/2 as unbiased estimator of θ. I'm stuck and confused need some help.
Thank u.
One way is by using Cramer-Rao Lower Bound This will also tell you whether it is attained.