The probability generating function of empty cell variable in a randomized occupancy problem |
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| Authors: | V.V. Menon B. Prasad |
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| Affiliation: | 1. Institute of Technology , Banaras Hindu University , Varanasi , 221005 , India;2. Directorate of Economics and Statistics , Indian Statistical Service , Research Officer, Ministry of Agriculture, India |
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| Abstract: | Let Mo denote the number of empty cells when n distinguishable balls are distributed independently and at random in ra cells such that each ball stays with probability p in its cell, and falls through with probability 1-p. We find the probability generating function of Mo by solving a partial differential equation satisfied by a suitable generating function. The corresponding function for the classical case p = 1 is well-known, but obtained by different methods. |
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| Keywords: | classical occupancy problem randomized occupancy problem empty cells characteristic function probability generating function |
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