random variable

Question

A random variable is defined as a process or variable with a numerical outcome. Which of the following are random variables? (please explain the answer as it is very confusing to me) ty

1. The amount of rain, in inches, that will fall next Friday in Dallas, TX.
2. The major of a randomly drawn student from Arizona State University.
3. The number of books purchased next year by your local library.

Answer 1

Based on the definition you've provided along with your question, you don't actually need to know anything about the process that produces the outcome of a random variable - you only need to verify that its value is numerical (quantitative) rather than some other type. Let's look through the answer choices:

1. "The amount of rain, in inches..." - We need look no further for this one; the key word "amount", along with the specified unit, signals a numerical value.
2. "The major of a randomly drawn student..." - You might be tempted to choose this one, since it includes the word "random", but notice that a student's major isn't a numerical value; even if the major options at ASU were in the form of Major 1, Major 2, etc., those numbers would merely be labels, rather than representing a quantity of something.
3. "The number of books purchased" - once again we have a keyword here, this time even more closely associated with the requirement that a random variable's outcome be numerical.

Keep in mind that you're not being asked to make any distinction between e.g. random vs. deterministic processes. Regardless of how the outcome was produced, if and only if its value is numerical, the variable can be considered a random variable.