Upper bounds for bivariate Bonferroni-type inequalities using consecutive events

摘要

Let $ A_1 , A_2, ldots, A_m $ and $B_1 , B_2, ldots, B_n$ be two sequences of events on the same probability space. Let $X = X_m (A)$ and $ Y = Y_n (B)$, respectively, denote the numbers of those $ A_i $'s and $ B_j $'s which occur. We establish new bivariate Bonferroni-type inequalities using consecutive events and deduce a known result.