Every <cumulative distribution function> is \b[nondecreasing, right-continuous, valued in $[0,1]$, and has limits $0$ at $-\infty$ and $1$ at $+\infty$]. For a continuous <random variable> it is continuous. When a <probability density function> exists, it is in fact absolutely continuous, with nonnegative <derivative> almost everywhere.

Solution

Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Discrete mathematics, continuous mathematics, and probability / Probability / 9 / a / ii / Solution

 Solution (source code)