Corpus ID: 162168623

A Short Note on the Average Maximal Number of Balls in a Bin

@article{Michelen2020ASN,
  title={A Short Note on the Average Maximal Number of Balls in a Bin},
  author={M. Michelen},
  journal={J. Integer Seq.},
  year={2020},
  volume={23},
  pages={20.1.7}
}
  • M. Michelen
  • Published 2020
  • Mathematics, Computer Science
  • J. Integer Seq.
We analyze the asymptotic behavior of the average maximal number of balls in a bin obtained by throwing uniformly at random $r$ balls without replacement into $n$ bins, $T$ times. Writing the expected maximum as $\frac{r}{n}T+ C_{n,r}\sqrt{T} + o(\sqrt{T})$, a recent preprint of Behrouzi-Far and Zeilberger asks for an explicit expression for $C_{n,r}$ in terms of $n,r$ and $\pi$. In this short note, we find an expression for $C_{n,r}$ in terms of $n, r$ and the expected maximum of $n… Expand
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References

SHOWING 1-9 OF 9 REFERENCES
On the Average Maximal Number of Balls in a Bin Resulting from Throwing r Balls into n Bins T times
  • 2
  • Highly Influential
  • PDF
The Probabilistic Method
  • 5,874
  • PDF
Probability: Theory and Examples
  • 4,883
  • PDF
Expectation of maximum of multivariate gaussian
  • MathOverflow. URL:https://mathoverflow.net/q/332113
  • 2019
Order Statistics
  • H. A. David
  • Computer Science
  • International Encyclopedia of Statistical Science
  • 2011
  • 1,121
Expected value for maximum of a normal random variable. Mathematics Stack Exchange posting
  • Available at https://math.stackexchange.com/q/510580
  • 2010
Probability: theory and examples, volume 31 of Cambridge Series in Statistical and Probabilistic Mathematics
  • 2010
Expected value for maximum of a normal random variable. Mathematics Stack Exchange. URL:https://math.stackexchange.com/q/510580 (version: 2013-10-01)
  • Dept. of Mathematics, University of Pennsylvania,
  • 1910