Final answer:
The claim regarding discrete random variables is false; they have countable values, unlike continuous random variables, which have uncountable, measured values and require probability assessments over a range.
Step-by-step explanation:
The statement "Discrete random variables take on values across a continuum." is false. Discrete random variables have countable values, such as the number of red balls or the number of heads tossed. In contrast, continuous random variables have uncountable values that are measured, not counted, like temperatures or heights.
Key characteristics of a discrete probability distribution include:
- Each probability is between zero and one, inclusive.
- The sum of the probabilities is one.
With continuous random variables, probabilities are assessed over a range rather than for exact values since they can take on an infinite number of values within a given interval.