Geometric minimum law
= Geometric minimum law
{title2=$\min_i X_i\sim\operatorname{Geom}\!\left(1-\prod_i(1-p_i)\right)$}
For independent positive-support <geometric random variables> with success probabilities $p_i$, all must exceed $k$ for their minimum to exceed $k$. The resulting <survival function> is $\prod_i(1-p_i)^k$. This is the positive-support <geometric distribution> with the displayed success probability. Independence is needed for multiplying the survival probabilities.