CDF for continuous random variables

• Definition: Let \(X\) be a continuous random variable with sample space \(\Omega = \mathbb{R}\). The cumulative distribution function (CDF) of \(X\) is

\[F_X(x) = \mathbb{P}[X\leq x] = \int\limits_{-\infty}^{\infty} f_X(x')\; dx'\]