User:Allenthar

The distribution $$F(x) =\prod_{i=1}^n F_{i}(x)$$ can be generated from $$F(x) = P(max(F_{1},...,F_{n}) \le k)$$ because the product of independent RV's are the same as the max of the RV's. If the max probability of all of the $$F_{i}$$'s is less than k, then all of the individual $$F_{i}$$'s must be less than k.