User:Allenthar
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The distribution <math>F(x) =\prod_{i=1}^n F_{i}(x)<math> can be generated from <math>F(x) = P(max(F_{1},...,F_{n}) \le k)<math> 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 <math>F_{i}<math>'s is less than k, then all of the individual <math>F_{i}<math>'s must be less than k.