# Random Variable

## Definition

A **Random Variable** (also *Stochastic Variable*) is a variable whose values depend on the outcome of a random (uncertain) phenomenon. In Risk Management random variables are the core Quantitative Model through which one represents Risk and its *realization* e.g. as risk events.

The *domain* (range) of a random variable is called a sample space. It is the set of possible outcomes of the random phenomenon which may be represented by any number of mathematical variables (continuous, discrete, categorical etc). In the case of a coin toss, only two possible outcomes are possible (heads or tails) indicating a binary variable

The *likelihood* of the random variable taking concrete values is governed by its probability distribution, which in risk management is often denoted as the Risk Distribution.