Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Discrete mathematics, continuous mathematics, and probability (resit) / 9 / b / i

Since $X$ is nonnegative, $F_X(x)=0$ for $x<0$. For $x\ge 0$, use $\frac{d}{dt}{e}^{-t^2/2}=-t{e}^{-t^2/2}$ to obtainThus the cumulative distribution function isIn particular it tends to one as $x\to \infty$, confirming normalization of this unit-scale Rayleigh distribution.