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Summary

Mean-value formulae for important characteristics (e.g. volume, surface area, etc.) of the common intersection of randomly placed point-sets are derived under the condition that the basic probability distribution of the underlying model is either motion-invariant or translation-invariant (the orientation of the generating sets in this latter case being known). Various special cases are discussed, some of them leading to a new derivation of known results of geometrical probability theory. The expected value of the probability that an arbitrary point is covered by the random intersection-set is also determined.

Randomly Generated Sets, Geometrical Probability, Mean-Value Formulae for Shape Parmeters

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