A variable that can take a certain set of values with given probabilities. Formalized using a Probability space as a map $X:\Omega \to \mathbb{R}$ such that the image $X(\Omega)$ is measurable and $X^{-1}(x) \in \mathcal{F}$ (the event space) $\forall x$ in the image of $X$. This allows to consider $P({X \in A})$ for an $A \in \mathcal{F}$

Two main types:

• Discrete random variable
• Continuous random variable