I am trying to derive the Cramer-Rao lower bound for $Var(\hat{\theta})$ given that we already know $\mathbb{E}[U]=0$, $Var(U)=I(\theta)$ and $\mathbb{E}[\hat{\theta}U]=1$. I am struggling with using the last fact, I know that the CRLB will be equal to $1/I(\theta)$ but can’t figure out how to use what is given to find this, any help would be much appreciated.
2026-02-23 11:43:40.1771847020
Derive Cramer-Rao lower bound for $Var(\hat{\theta})$ given that $\mathbb{E}[\hat{\theta}U]=1$
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