# Correct notation for probability

Suppose I have a sequence of $$n$$ iid random variables (RV) $$X_1,X_2,...,X_n$$ I want to denote the probability of at least one of those RV being lower than a threshold $$x$$. Is this notation correct?

$$P(X_1,X_2,...,X_n

Or does this mean probability of all RV being lower than $$x$$?

• I would write $P(\min\{X_1,X_2,...,X_n\}<x)$ – callculus Mar 24 at 13:16

$$P(X_1, X_2, \ldots, X_n means all RV being lesser than $$x$$.
The desired event for which you want to denote its probability sounds ad hoc, so I wouldn't expect it to be only one way of denoting it. One way (perhaps the most intuitive) is as callculus suggests: $$P(\min\{X_i \mid 1 \leq i \leq n\} . Another possibility is $$P(\{i \mid X_i , or $$P(\#\{i \mid X_i 0)$$.