Given X∼Uniform(0,1)X \sim \text{Uniform}(0, 1)X∼Uniform(0,1), what is the PDF of Y=X2Y = X^2Y=X2?
f_Y(y) = \frac{1}{2\sqrt{y}}, 0 < y < 1
f_Y(y) = 2y, 0 < y < 1
f_Y(y) = \sqrt{y}, 0 < y < 1
f_Y(y) = 1, 0 < y < 1