Final answer:
The statement about a random variable being able to take on a number of possible outcomes is true. Random variables come in two types: discrete, which have countable outcomes, and continuous, which are measured and have uncountable outcomes. The distribution of a discrete random variable lists all possible values and their associated probabilities, which sum to one.
Step-by-step explanation:
The statement "A random variable is a parameter that can take on a number of possible outcomes" is true. A random variable is indeed a variable whose possible values represent outcomes of a stochastic, or random, process. More specifically, they are a quantitative representation of the results of a probability experiment.
There are two types of random variables: discrete and continuous. Discrete random variables have countable outcomes, like the number of heads when flipping coins. Continuous random variables, on the other hand, have uncountable outcomes and are typically measured, such as the temperature of a randomly selected day or the height of a randomly selected student. When listing the values of a discrete random variable X, one would count the possible outcomes (e.g., 0, 1, 2, ... heads), while for a continuous random variable, the values would involve a range of measurements.
The distribution of a discrete random variable is a list of all possible values and the probabilities associated with each value. The probabilities must add up to one. This distribution can be represented in tabular form or graphically, with each value on the x-axis and corresponding probability on the y-axis of a graph.