For a fair die that was rolled twice:
$ R^2$ with R ={1,2,3,4,5,6} and the common distribution function is 1/6 for all possible outcomes
Given that X = min(X1,X2) where X1 is one outcome and X2 is the other possible outcome
Also let F(x) be the CDF:
F(x) = P(X≤x)
= 1 - P(X<x)
= 1 - P(X1>x, X2>x)
= 1 - P(X1>x)*P(X2>x)
= 1 - F(x1)*F(x2)
Therefore, F(y) = 1 - [\(\frac{1}{6}\)*\(\frac{1}{6}\)]
or F(x) = 1 - \(\frac{1}{36}\)