International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 60, Pages 3827-3840
doi:10.1155/S0161171203110101
On the birthday problem: Some generalizations and applications
P.N. Rathie
and P. Zörnig
Departamento de Estatística, Instituto de Ciências Exatas, Universidade de Brasília, Brasília, DF 70910-900, Brazil
Abstract
We study the birthday problem and some possible extensions. We discuss the unimodality of the corresponding exact probability distribution and express the moments and generating functions by means of confluent hypergeometric functions U(−;−;−) which are computable using the software Mathematica. The distribution is generalized in two possible directions, one of them consists in considering a random graph with a single attracting center. Possible applications are also indicated.