### Random variable definition

A random variable is a variable that is subject to random variations so that it can take on multiple different values, each with an associated probability.

A random variable could be discrete, such as in the result of rolling a six-sided die. A random variable $X$ modeling the result of such an experiment would take on a value from the set $\{1, 2, 3, 4, 5, 6\}$, each with probability $1/6$.

A random variable could also be continuous, such as in the result of randomly choosing a number between 0 and 1. A random variable modeling the result of such an experiment could take on any real number in the interval $[0,1]$, where each number would be equally likely.

For the concepts behind random variables, see the page on the idea of a probability distribution.