Prove this version of the Bonferroni inequality: P(\cap^{n}_{i=1} A_{i})\geq 1-\sum_{i=1}^n P(A_{i}^{c})(Use Venn diagrams if you wish.) In the contex

FobelloE 2021-07-03 Answered

Prove this version of the Bonferroni inequality: \(\displaystyle{P}{\left(\cap^{{{n}}}_{i=1}{A}_{{{i}}}\right)}\geq{1}-{\sum_{{{i}={1}}}^{{n}}}{P}{\left({{A}_{{{i}}}^{{{c}}}}\right.})\)(Use Venn diagrams if you wish.) In the context of simultaneous confidence intervals, what is Ai and what is \(\displaystyle{A}^{{{c}}}_{i}\)?

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FieniChoonin
Answered 2021-07-04 Author has 23752 answers
Using the induction, we managed to prove the Bonferroni inequality.
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