Distribution functions of independent minima and maxima
= Distribution functions of independent minima and maxima
{title2=$F_{\min}=1-(1-F_X)(1-F_Y),\quad F_{\max}=F_XF_Y$}
Independence factors the events that both variables exceed a threshold or both lie below it. This gives the two <cumulative distribution functions> above, including for distributions with atoms. The minimum formula is most naturally expressed through survival <probabilities>, while the maximum formula uses the CDFs directly.