Let, $X_1,X_2,\dots, X_n$ are random sample from $\text{Bin}(1,p)$. Find an unbiased estimator of $\dfrac{1}{p}$.
If I start with $T$ be an estimator, then $$\sum_{k=0}^{n}T(k)\space \binom{n}{k}p^k(1-p)^{n-k}=\frac{1}{p}$$
Multiplying $p$ both side, and taking $t=\dfrac{p}{1-p}$, I found that coefficient of $t^0$ do not match in both side. Hence we can not find $T$ in this way.
My question is, is there any alternative way to find an unbiased estimator of $1/p$ ? Any help appreciated!