• Rao-Blackwell Theorem in Point Estimation:
• The Rao-Blackwell theorem states that if $T$ is a sufficient statistic for a parameter $\theta$, and $U$ is any unbiased estimator of $\theta$, then the conditional expectation:

is an unbiased estimator of $\theta$ whose variance is strictly less than or equal to the variance of $U$ (i.e., $\text{Var}(\phi(T)) \le \text{Var}(U)$).

• Furthermore, by the Lehmann-Scheffé theorem, if the sufficient statistic $T$ is also complete, then $\phi(T)$ is the unique Uniformly Minimum Variance Unbiased Estimator (UMVUE).
• Other Options:
• Central Limit Theorem: Describes asymptotic normality of sample means.
• Cramér-Rao inequality: Provides a theoretical lower bound for the variance of unbiased estimators.
• Neyman-Pearson lemma: Constructs Most Powerful tests in hypothesis testing.
• Conclusion: Rao-Blackwell theorem (Option 3).

Correct option: (3) Rao-Blackwell theorem