We want to compute the area of the unit circle to estimate it, i.e., compute Uzz+21 1dxdy = S 1-x2 /1-22 dydx = 4 fo v1 - x2 dx by a Monte-Carlo method. We drew 10^4 values of U; from a uniform distribution and computed X; = 4,/1 - U2 and we got Xn = 2 Et Xi ~3.15 o n n- Zi=1(Xn - Xi)? ~ 0.7922 Give a 95% confidence interval for it. Give a lower bound of this interval in this question (up to two decimals)