User:Allenthar

The distribution $F(x)=\prod _{i=1}^{n}F_{i}(x)$ can be generated from $F(x)=P(max(F_{1},...,F_{n})\leq k)$ 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.