Summary
LetA 1,A 2, ⋯,A m ,C 1,C 2, ⋯,C n be events on a given probability speace. LetV m andU n , respectively, be the numbers among theA i 's andC j 's which occur.Upper and lower bounds ofP(V m ⩾1, U n ⩾1) are obtained by means of the bivariate binomial moments. These extend recent univariate optimal Bonferroni-type inequalities.
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Lee, MY. Bivariate Bonferroni inequalities. Aeq. Math. 44, 220–225 (1992). https://doi.org/10.1007/BF01830980
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DOI: https://doi.org/10.1007/BF01830980