Given X∼Normal(0,1)X \sim \text{Normal}(0, 1)X∼Normal(0,1), what is the PDF of Y=∣X∣Y = |X|Y=∣X∣?
2πe−y2/2\sqrt{\frac{2}{\pi}} e^{-y^2/2}π2e−y2/2 for y>0y > 0y>0
12πe−y2/2\frac{1}{\sqrt{2\pi}} e^{-y^2/2}2π1e−y2/2 for y>0y > 0y>0
2πye−y2/2\sqrt{\frac{2}{\pi}} y e^{-y^2/2}π2ye−y2/2 for y>0y > 0y>0
22πe−y2/2\frac{2}{\sqrt{2\pi}} e^{-y^2/2}2π2e−y2/2 for y>0y > 0y>0