Continuous Random Variable

Definition

A continuous random variable $X$ is a random variable whose cumulative distribution function $F(x) = \mathbb{P}(X \leq x)$ is continuous. Equivalently, $X$ has a Probability Density Function (PDF) $f$ such that

$$ F(x) = \int_{-\infty}^{x} f(t)\, dt. $$

For any single point, $\mathbb{P}(X = x) = 0$.

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Related

• STA414
• Probability Density Function (PDF)
• Discrete Random Variable
• Valid Probability Density Function