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Bounds represent the points with which data cannot exceed, such as minima or maxima.

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Expectation of first of moment of symmetric r.v. in terms of variance

You can actually develop your first example a little more to refute this conjecture, that is put some mass at $0$. Let $X$ be the random variable such that $P[X = 0] = 1 - p$, $P[X = -1] = P[X = 1] = …
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6 votes

Upper bound for 1-Wasserstein distance between standard uniform and other distribution on $[...

Your own solution is on the right track, yet is not fully rigorous (or it is still incomplete). Below is a two-step proof that has its root on standard real analysis principles. Step 1: $F$ is a simpl …
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