Definition:Random Variable/Continuous

Definition

Let $\mathcal E$ be an experiment with a probability space $\struct {\Omega, \Sigma, \Pr}$.

A continuous random variable on $\struct {\Omega, \Sigma, \Pr}$ is a random variable $X: \Omega \to \R$ whose cumulative distribution function is continuous for all $x \in \R$.

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: continuous random variable