The validity of the assumption of Gaussian statistics, a basis for the validity of use of the radiative transfer equation and for a lot of current astrophysical maser theories, is investigated. For tractability the investigation in this paper is confined to astrophysical linear masers, which are very important to astrophysical maser theories. It is found that for those masers the assumption of Gaussian statistics and therefore the use of the radiative transfer equation are not precise in saturated regions whereas they are valid in unsaturated ones. This will be very significant to the study of astrophysical masers.