Let X∼Uniform(0,1)X \sim \text{Uniform}(0, 1)X∼Uniform(0,1). Find the PDF of Y=X2Y = X^2Y=X2.
fY(y)=1f_Y(y) = 1fY(y)=1 for 0<y<10 < y < 10<y<1
fY(y)=12yf_Y(y) = \frac{1}{2\sqrt{y}}fY(y)=2y1 for 0<y<10 < y < 10<y<1
fY(y)=2yf_Y(y) = 2yfY(y)=2y for 0<y<10 < y < 10<y<1
fY(y)=yf_Y(y) = \sqrt{y}fY(y)=y for 0<y<10 < y < 10<y<1