What is a random variable?

A random variable represents a numerical outcome of a random phenomenon, meaning it can take on different values based on the outcome of a random process. Because of this inherent uncertainty, the future value of a random variable is not fixed or deterministic; instead, it is characterized by a probability distribution, which outlines the likelihood of various possible outcomes.

For example, when rolling a die, the outcome (the value showing on the top face) is a random variable since it can be any number from one to six, each with different probabilities. This uncertainty is what defines a random variable.

The other options describe characteristics that do not align with the definition of a random variable. A variable with a constant future value does not incorporate randomness, thus cannot be a random variable. A variable that cannot be measured does not fit the concept of a random variable, as random variables are typically quantified in some way. Lastly, a variable that only takes integers would be a specific type of random variable (discrete), but not all random variables are restricted to integer values; some can take any value within a range, making them continuous.