We propose a method of simulation that is based on the averaging of formal
solutions of the transfer equation by taking the integral by the Monte Carl
o method. This method is used to compute two models, which correspond to th
e limiting cases of hot gas and cold background radiation and of hot backgr
ound radiation and cold gas, for E-methanol emission from a compact homogen
eous spherical region. We analyze model level populations by using rotation
al diagrams in the limiting cases mentioned above. Model optical depths of
the lines with frequencies below 300 GHz up to J = 11 inclusive are given.