A 6 MeV electron beam incident on a 0.1 mm foil of gold has a Gaussian-like radial profile (centered on the beam axis) at the exit of the foil with an FWHM of 1 mm. (a) Determine the variance of the distribution and (b) perform a Monte Carlo sampling of the transverse coordinates, making a histogram of the sampled values. As verification, compare with the corresponding analyt- ically determined Gaussian distribution. Answer: Gaussian = 0.425 mm (FWHM = 2.3548 6). Sampling is made using Eq. (8.19) in the textbook.