Estimate total balls based on the ball count in a bin

24 Views Asked by At

I am struggling to formalise the following problem. We randomly spread $m$ balls into $n$ bins. $m$ is unknown, but $n$ is known in advance. Now, we sample the first bin (or any bin) and see it has $k$ balls. Can we say something about $E[m]$ in that case? Can we know how $m$ is distributed?