Somebody rolls $n$ dice (each has $6$ sides, perfectly balanced) and tells me $k$ of them were $6$s. I'm trying to estimate $n$ based on $k$.
I think a good estimate for $n$ is $6k$ (or at least it makes sense to me intuitively) but I can't figure out:
1) how to prove that it isn't biased
2) how to compute the variance of this estimator.
Sorry if similar questions were asked before, it seems so simple that it must have been answered somewhere else but I couldn't find it.