> [!definition] > > Let $X$ be a continuous [[Random Variable|random variable]], and let $f \in L^1$ be an [[Integrable Function|integrable function]] such that the [[Probability|probability]] can be evaluated as an [[Integral|integral]] > $ > P(X \in B) = \int_B f(t)dt \quad B \in \cb > $ > Then $f$ is the **probability distribution function** of $X$. Any two such probability distribution functions are equal [[Almost Everywhere|a.e.]]