Poisson randomization in occupancy problems |
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Authors: | Mauro Cerasoli |
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Affiliation: | Istituto di Matematica, Università, L''Aquila, 67100-Italy |
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Abstract: | In occupancy problems we randomize the number of balls with a Poisson process of intensity α. Thus some classical formulas are very easily demonstrated and generalized with the aid of inclusion-exclusion principle. Then we give a general theorem to calculate the distributions and moments of particular random variables or waiting times when infinite balls are considered. This theorem can be applied to the well-known birthday and coupon collectors problems. |
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