I am very new to Rao Blackwell theorem.
It says that, if $\delta(X)$ is an unbiased estimator for a parameter $\theta$, then the estimator $T_0(X)=E\left(\delta|T\right)$, whete $T(X)$ is a sufficient statistic is also unbiased with variance no more than variance of $\delta(X)$.
So i was trying an example with Poisson distribution:
Its PMF is $$P(X=x)=\frac{e^{-\lambda}\lambda^x}{x!} \:x>0,\lambda>0$$
Let $X_1,X_2,..X_n \sim poisson(\lambda) $
Let $\delta(X)=X_1$ and this is obviously an unbiased estimator for $\lambda$.
Also By factorization theorem $T(X)=\sum_{i=1}^{n}X_i$ is a sufficient statistic.
Now we have: $$T_0=E\left(X_1|T=t\right)$$
Now how can i proceed to Rao blackwellization?