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: Suppose a box contains m balls, numbered from 1 to m. A random number of balls are drawn from the box, their numbers are noted, and the balls are then returned to the box. This is done repeatedly, with the sample sizes being iid. Let X be the number of samples needed to see all the balls. This paper derives a simple but typically very accurate approximation for EX in terms of the sample size distribution. The justification of the approximation formula uses Wald's identity and Markov-chain coupling.

How Many IID Samples Does it Take to See all the Balls in a Box?