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February, 1995 How Many IID Samples Does it Take to See all the Balls in a Box?
Thomas M. Sellke
Ann. Appl. Probab. 5(1): 294-309 (February, 1995). DOI: 10.1214/aoap/1177004841


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 uses Markov-chain coupling to derive a simple but typically very accurate approximation for $EX$ in terms of the sample size distribution. The approximation formula generalizes the formula found by Polya for the special case of fixed sample sizes.


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Thomas M. Sellke. "How Many IID Samples Does it Take to See all the Balls in a Box?." Ann. Appl. Probab. 5 (1) 294 - 309, February, 1995.


Published: February, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0823.60054
MathSciNet: MR1325054
Digital Object Identifier: 10.1214/aoap/1177004841

Primary: 60J10

Keywords: Coupon collector's problem , Markov chains , Markov-chain coupling

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.5 • No. 1 • February, 1995
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