Bonferroni inequalities

Let E(1), E(2),,E(n) be events in a sample space. Define


and for 2<kn,


where the summation is taken over all ordered k-tuples of distinct integers.

For odd k, 1kn,


and for even k, 2kn,


Remark When k=1, the Bonferroni inequalityMathworldPlanetmath is also known as the union bound. When k=n, we have an equality, also known as the inclusion-exclusion principleMathworldPlanetmath.

Title Bonferroni inequalities
Canonical name BonferroniInequalities
Date of creation 2013-03-22 14:30:40
Last modified on 2013-03-22 14:30:40
Owner kshum (5987)
Last modified by kshum (5987)
Numerical id 9
Author kshum (5987)
Entry type Theorem
Classification msc 60A99
Related topic BrunsPureSieve
Defines union bound