In the context of the confidence interval for parameter $\theta$ with confidence level $1-\alpha$ I was always dealing with such formulation,
$P(\theta \in \mathbb{T}_n)=1-\alpha$,
with the "=" sign. However, on Wikipedia, I found the following definition,
$P(\theta \in \mathbb{T}_n) \ge 1-\alpha$,
which I also see in some books and publications. The author has written on Wikipedia that such formulation "is useful (...) when dealing with discrete distributions". I do not fully understand why such a formulation is more appropriate for discrete distributions, or why the first one does not work. I read about the concept of conservative intervals which are constructed in a way to fulfill the second definition, and I understand that sometimes it is more convenient to define the ci in such a way. However, still, I do not understand why such a formulation is used in general for discrete rvs.