Let X∼Normal(0,1)X \sim \text{Normal}(0, 1)X∼Normal(0,1). What is the probability density function of Y=X4Y = X^4Y=X4?
fY(y)=12πy−3/4e−y/2,y>0f_Y(y) = \frac{1}{\sqrt{2\pi}} y^{-3/4} e^{-\sqrt{y}/2}, y > 0fY(y)=2π1y−3/4e−y/2,y>0
fY(y)=12πy−3/4e−y,y>0f_Y(y) = \frac{1}{\sqrt{2\pi}} y^{-3/4} e^{-\sqrt{y}}, y > 0fY(y)=2π1y−3/4e−y,y>0
fY(y)=12πy−1/2e−y/2,y>0f_Y(y) = \frac{1}{\sqrt{2\pi}} y^{-1/2} e^{-y/2}, y > 0fY(y)=2π1y−1/2e−y/2,y>0