Question

In a ___________, a random variable can take any value in a specified range.

Answer 1

The answer is "c. continuous probability distribution."

"Continuous" means it is a subset of the real numbers set: it can take any value in a specified range. For example, if you break at random a stick with a given length of 12 cm, and then measure the shortest piece, you can get any value in the range (0 cm, 6 cm). This is a continuous random variable.

A random variable is said to be "discrete" if it can only take values from a finite (or countably infinite) set. For example, if you roll a dice, you can get only 1, 2, ..., 6. But you cannot get any vaue in the range [1, 6], because the value must be an integer (e.g., you cannot get the vaue 2.5). This is a discrete random variable.

A somewhat technical explanation:

- A random variable is a mapping from a event space to a number set: it associates a number (a value of the variable) with every event.

- The random variable is said to be continuous if it maps events to numbers from a subset of the set of real numbers.

- The probability distributions corresponding to continuous random variables are called continuous probability distributions.