Given a random experiment with sample space \(S\text{,}\) a function \(X\) mapping each element of \(S\) to a unique real number is called a random variable. For each element s from the sample space \(S\text{,}\) denote this function by
\begin{equation*}
X(s) = x
\end{equation*}
and let \(R\) be the range of \(X.\)