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The distribution of the number of empty cells in a generalized random allocation scheme. (English) Zbl 0633.60016

Random graphs ’85, Lect. 2nd Int. Semin., Poznań/Pol. 1985, Ann. Discrete Math. 33, 77-90 (1987).
[For the entire collection see Zbl 0626.00008.]
Consider an \(m\times N\) matrix of zeros and ones. Each row consists of n ones put at random places and independent of the other rows. By independent Bernoulli trials each one is changed into zero, the same probability for each. Let the random variable S be the number of columns with no ones.
Expressions for the exact distribution, moments and factorial moment generating function of S are given. It is proved that S has a representation as a sum of N independent Bernoulli random variables. Using convergence of factorial cumulants, sufficient conditions are given for asymptotic normality of S as \(N\to \infty\).
Reviewer: L.Holst

MSC:

60C05 Combinatorial probability
60F05 Central limit and other weak theorems

Citations:

Zbl 0626.00008