Random Variable

A Random Variable is a Function $X$ that maps each Outcome $\omega$ of the Sample Space $S$ of a Random Experiment to a Real Number $x\in \mathbb{R}$

$$X:\omega \in S\to x\in \mathbb{R}$$

• the Random Variable is always denoted with a capital letter, and the real number is the corresponding lowercase letter, e.g. $X$ and $x$, $Y$ and $y$, etc.
• a Random Variable can be discrete or continuous