Definition:Random Variable/Continuous

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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 $x \in \R$.


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