I was going through the article coping with copulas. The following situation was considered there. A die is rolled twice. $X_1$ is the random variable representing the minimum of the two rolls, $X_2$ is the random variable representing the maximum of the two rolls. The probability distribution of an individual thrown is given by $F(x) = F(X \le x)$. I believe $F(x) = \frac{x}{6}$.
The joint probability distribution $\tilde{F}$ of $X_1, X_2$ is mentioned as:
$\tilde{F}(X_1 \le x_1, X_2 \le x_2) = F(\min \{x_1,x_2 \}) \cdot F(x_2) - F(\min \{x_1,x_2 \})^2$. I am able to find the numerical values by tabulating the outcomes, but how to arrive at the above formula?
Also I couldn't get the formatting of the formula right as much as I tried.