Let X∼N(0,σ2)X \sim N(0, \sigma^2)X∼N(0,σ2) and Y=∣X∣Y = |X|Y=∣X∣. What is the PDF of YYY?
fY(y)=2πσ2e−y2/(2σ2)f_Y(y) = \sqrt{\frac{2}{\pi\sigma^2}} e^{-y^2/(2\sigma^2)}fY(y)=πσ22e−y2/(2σ2)
fY(y)=1σ2πe−y2/(2σ2)f_Y(y) = \frac{1}{\sigma\sqrt{2\pi}} e^{-y^2/(2\sigma^2)}fY(y)=σ2π1e−y2/(2σ2)
fY(y)=2σ2πe−y2/(2σ2)f_Y(y) = \frac{2}{\sigma\sqrt{2\pi}} e^{-y^2/(2\sigma^2)}fY(y)=σ2π2e−y2/(2σ2)
fY(y)=12πe−y/(2σ)f_Y(y) = \frac{1}{\sqrt{2\pi}} e^{-y/(2\sigma)}fY(y)=2π1e−y/(2σ)