A Probability Bound for the Union of Random Sets.
WASHINGTON UNIV ST LOUIS MO DEPT OF COMPUTER SCIENCE
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Given a collection of independent random subsets of a finite set N satisfying certain symmetry conditions, there is an easily-computed estimate for the probability their union is N. It is shown this estimate is a valid upper bound, provided certain functions associated with the distribution of the random size of the subsets have concave logarithms. Examples are given. The results complement known results in the theory of reliability on sums of random variables with increasing failure rates.
- Statistics and Probability