$$ g(x) = A e^{\large -\frac{(x-\overline{x})^2}{2\sigma^2}} $$ $$ A = \sqrt{2\pi} \sigma N \Delta x $$ $$ z_1 = \sqrt{-2 \ln x_1} \cos(2\pi x_2) $$ $$ z_2 = \sqrt{-2 \ln x_1} \sin(2\pi x_2) $$