A set of all possible values of a discrete random variable is countable, because the variable can assume values only at specific points on a scale of values, with inevitable gaps in between.

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A discrete random variable can only take on a finite or countably infinite set of values. Therefore, the set of all possible values is also countable. This is because the values are specific points on a scale, and there are only a finite or countable number of these points, with gaps in between.

A Set of All Possible Values of a Discrete Random