Given $X_1,X_2,...X_n$ IID from a Bernoulli distribution while $n>2$.
If I want to find an unbiased estimator for $$(1-p)p$$ as a function of $X_1, X_2$ and the use Rao Blackwell theorem
I realize this is the $\mathbb{E}[Var(P)]$ not sure if this implies anything instantly.
My question is what is the pmf for bernouli here to get the unbiased estimator?
What I thought of so far:
$\theta = p(1-p)$
$\mathbb{E}[\hat{\theta}] = \sum_{i=0}^{\infty}T(i)(1-p)^ip^i = p(1-p)$
Any hints are appreciated!