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1690s, Scottish, "aggressive, boisterous," probably from rand "to rave," an obsolete variant of rant (v.). In the original sense especially of beggars, "and probably implying vagrant habits as well as rude behavior" [OED]. Sense of "lewd, lustful" first recorded 1847. Related: Randiness.
[1847+; origin unknown; various dialect senses suggest a possible derivation fr ''wild movement,'' ''boisterousness,'' ''wantonness'']