I have followed the CRLB derivation, and I couldn't figure out why -
If f(x; θ) be a probability density with continuous parameter θ, and X1, . . . , Xn be independent random variables with density f(x; θ), and Θ(X1, . . . ,Xn) be an unbiased estimator of θ.
Why does the estimator, Θ, is independent of θ (the param to be estimated)?
Θ is a function of X1,...,Xn, and in the pdf of each one of them θ appears as a param. Doesn't it imply that Θ is also dependent on θ?