Which of the following best captures the defining difference between a discrete random variable and a continuous random variable?

Discrete random variables are described by probability density functions which allocate probability across a continuous range, while continuous random variables are always uniform over an interval and have equal probability at every point.

Discrete variables always have integer values and their probabilities are given by densities over intervals, whereas continuous variables have probabilities assigned to individual points and are represented by bar graphs spanning those points.

A discrete random variable takes values from a countable set (often listed) and is represented by a probability mass function or bars, while a continuous random variable can take any value in an interval and is described by a probability density function.

A discrete random variable can take an infinite number of values in an interval and is graphed as a shaded region, while a continuous random variable only takes a finite set of possible values that are shown in a table with their probabilities.