Distribution of τ_max vs. energy for three different treatments of the statistical errors (systematic errors are neglected). Red triangles: only statistical errors in the H.E.S.S. spectrum are taken into account; black circles: statistical errors in the Fermi-LAT and H.E.S.S. fluxes are included in the linear approximation; blue open squares: statistical errors from Fermi-LAT and H.E.S.S. are included using the exact analytic solution derived here.