Which of the following is true about discrete random variables?

Discrete random variables are defined as those that can take on distinct, separate values, which can be counted. This includes whole numbers, such as 0, 1, 2, and so forth. While they can be finite or infinite in number, the critical aspect is that the values can be counted—hence, they can take on a countable number of distinct values.

For instance, the number of customers arriving at a store during a day is a discrete random variable because it can be expressed in whole numbers: you might have 0, 1, 2, or even many more customers, but you cannot have a fractional customer (like 2.3) in this context. This characteristic distinguishes discrete random variables from continuous random variables, which can take on any value within a given range and are not restricted to whole numbers.

The assertion that they can only take values of integers is too restrictive since discrete random variables can also take on other countable values, as long as those values are distinct and separate. Claiming that they are determined only by continuous processes is inaccurate, as discrete random variables arise from situations that are inherently countable and not tied to continuous phenomena. Lastly, saying they can take an infinite number of values might