Probability density functions, f_2D(p,ψ | I₀,p₀,ψ₀,Σ), with finite S/N on intensity, I₀/σ_I = 1, 2, and 5 (columns from left to right), computed for a given set of polarization parameters, ψ₀ = 0° and p₀ = 0.1 (dashed lines), and a S/N on the polarized intensity set to p₀/σ_p,G = 1. Correlation coefficients ρ_Q and ρ_U are set to zero. Various configurations of the covariance matrix are shown (rows). White crosses indicate the mean likelihood estimates of the PDF (). The contour levels are provided at 0.1, 1, 5, 10, 20, 50, 70, and 90% of the maximum of the distribution. The polarization fraction is here defined over both the negative and positive ranges, due to the noise of the intensity.