We have made a likelihood statistical analysis of the angular correlations in the COBE-DMR two-year sky maps by Monte Carlo simulation of the temperature fluctuations. We assume an open universe and consider the primordial power spectrum of Harrison-Zeldovich, P(k)=Ak. We find that the flatness of the universe is not implied by the data. The quadrupole normalization amplitude, Qrms-ps, is related to the density parameter, Ω, by Qrms_PS =10.67+55.81Ω— 128.59Ω2 + 81.26Ω3 μK. We have determined the probability distribution function (pdf) of Ω arising from cosmic plus sampling (i.e. 20° galactic cut) variance which generically shows a bimodal shape. The uncertainty as given by the rms is ≈0.35; therefore, to constrain Ω better, experiments sensitive to higher multipoles (l > 20) should be considered.