What is the PDF or CDF of $|X_1 - X_2|$ (absolute value of the difference of two variables). When both $X_1$ and $X_2$ has different Uniform distribution.
Note: We can look at the as the distribution of the range of 2 ordered-statistics; However, the formula I am aware of, is just for iid statistics (same distribution)
If $X_1$ and $X_2$ are uniformly distributed and independent, then $(X_1,X_2)$ is uniformly distributed on a rectangle, and $\mathbb{P}(|X_1-X_2|\leq t)$ can be determined by finding the area of intersection of the region between the lines $y=x+t$ and $y=x-t$ with this rectangle (divided by the total area of the rectangle of course). I'd try it first in the case when $X_1$ and $X_2$ are uniformly distributed on $[0,1]$.
If the two random variables are both real, then you'll get a random variable whose p.d.f. is a trapezoid. If the two random variables have the same uniform distribution, then the trapezoid will degenerate to a triangle.
