In all cases we can offset it with an addition... like -10+Random(11) would range from -10 to 10. But Random in its current form is confusing; one expects that the N will be included (11). Also, one would also expect that Random (1) would give boolean results (0 for false, 1 for true), but in fact you have to do Random(2) (gives 0 or 1).
Changing it to 1-indexed could also cause confusion; Random(2) would return 1 or 2, but not 0. Those used to the zero could easily get confused.
What I say is, decide on a convention and stick to it! Also explain it well in tooltip and in documentation.