Final answer:
The statement is True; a random variable can have multiple possible outcomes and is a key concept in probability and statistics.
Step-by-step explanation:
The statement "A random variable is a parameter that can take on a number of possible outcomes" is True. In statistics, a random variable (RV) represents a characteristic of interest that can take on a number of different outcomes, based on the results of a probability experiment.
These variables can be either discrete or continuous. Discrete random variables have countable outcomes, while continuous random variables have outcomes that are measurable and not countable.
Random variable notation often involves using uppercase letters like X or Y to denote the variable itself. The different outcomes of a random variable are represented by lowercase letters such as x or y. For instance, if a jar contains 3 marbles of different colors and we let X represent the color of a randomly chosen marble, then the possible values of x could be red, white, or blue, after conducting the experiment.
Discrete random variables have certain characteristics, such as their probabilities lying between zero and one, and the total sum of these probabilities being one. On the other hand, continuous random variables can represent a vast array of data in real-world situations, such as SAT scores, batting averages, or the duration of a telephone call. It's important to define the random variable accurately since its definition determines whether it is discrete or continuous.