Thread: pmf, MVUE

Let f=f(y;x),y>0 be a probability mass function that depends on the unknown parameter x, has continuous first and second order derivatives, and the support of f does not depend on the x.
1.show that the constant estimator x'=x, where x is the true value, is a minumum variance unbiased estimator for x.
2.what is the variance of x'?
3.and why the Cramer-Rao lower bound for f is not necessarily lower bound for x'=x?

you cannot estimate a parameter with itself.
The variance of that constant would be zero by the way.
and the expected value of a constant is that constant, so theta is unbiased for theta
but theta is not a statistic, it depends on the unknown paramter

but how can you explain that this estimator is the minimum variance unbiased estimator,this is true though ?