Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Discrete mathematics, probability and continuous mathematics / 9 / a / i / Solution

The cumulative distribution function is $F_X(x)=\mathbb{P}(X\le x)={\int }_{-\infty }^{x}f(u)du$. This formula uses the assumed probability density function; the density itself need not be a continuous function.