Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 4 / 28K / e / Solution

The accepted $Y$ has the half-normal distribution, so $Y=|G|$ in distribution for $G\sim N(0,1)$. Multiplying it by an independent random sign that is positive and negative with equal probabilities restores the two symmetric halves of the Gaussian density. Thus