In this paper we study the response of the linearized barotropic vorticity equation to stochastic perturbations of the frictional damping and the zonal mean flow. The stochastic parameterizations lead to multiplicative stochastic forcing. By explicitly solving the Fokker-Planck equation and the stochastic differential equation, this study goes beyond the already known effect of multiplicative noise on the mean Rossby wave response. It is found that the qualitative behavior of the system is a function of the multiplicative noise level if the frictional damping is perturbed. In particular, the effect of multiplicative noise in the damping is not simply a smoothing of the probability density function (PDF). Rather, multiplicative noise leads to a highly non-Gaussian distribution due to an intermittent behavior of the Rossby waves. This effect is not observed if the zonal mean flow is perturbed stochastically. This simple, yet realistic stochastic model can serve as a null hypothesis for the non-Gaussian behavior of atmospheric PDFs.