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$s$ balls are sampled and then replaced from/into a box with $N$ balls. On average, how many samplings are to be made until all of the balls have been taken at least once?

ps: this is not a homework problem. I’m trying to reduce the number of updates on parameters during a neural network’s optimization phase. I’m able to simulate this experiment and get a good numerical approximation, but doing so for every different value of $s$ and $N$ seems a little unclever.

L.B.
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  • Does this mean that each of the $s$ in one attempt are distinct? Or that they can have duplicates too? – Henry Jul 31 '19 at 21:53
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    See the various answers at https://math.stackexchange.com/questions/3278200/iteratively-replacing-3-chocolates-in-a-box-of-10 and https://mathoverflow.net/questions/229060/batched-coupon-collector-problem and https://math.stackexchange.com/questions/131664/coupon-collector-problem-with-batched-selections – Henry Jul 31 '19 at 22:05
  • @Henry Right on the spot! Thanks – L.B. Jul 31 '19 at 22:06

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