Suppose $Y_1, Y_2$ are from a random sample of the uniform distribution on $[0, 1]$. How do I compute the variance of the geometric mean of two points in the interval $[0, 1]$?
I know the geometric mean is $X=(Y_1 Y_2)^{1/2}$. I can't compute the variance since I'm not sure how to find the expected value of a radical.