Say $X,Y \sim U(0,1)$ be two independent uniform random variables, and $T=|X-Y|$. I would like to find the CDF of $M=\max(X,Y)$, $L=\min(X,Y)$, and $T$. I find the CDF of $M$ and $L$ as $$P(M\leq t ) = P(X\leq t)P(Y \leq t) =t^2$$ $$P(L \leq t) = 1-P(X\geq t ) P(Y\geq t) = 1-(1-t)^2$$ To find the CDF of $T$, I draw a rectangle with unit length and width, and compute the area within the region $|X-Y| \leq t$, which turns out to be $1-(1-t)^2$.
My question is how come the CDF of $L$ and $T$ are the same when one is the minimum of two uniform r.vs and the other is the absolute difference of two uniform r.vs? Is there something wrong with my computation? Thanks.