Top: conditional probability density (Equation (A1)) of the apparent color at each value of the velocity for an assumed linear intrinsic color–velocity trend μ_C(v) with slope of b = −0.02 mag (10³ km s⁻¹)⁻¹ (blue line) and an average dust reddening of τ/R_V = 0.1 mag. The solid red line is the color of the peak of P(O|v), and the dashed red lines are the 2.5% and 97.5% quantiles of P(O|v). This is shown for the residual intrinsic scatter of σ_C = 0.05 mag (left) and σ_C = 0.1 mag (right). Bottom: the joint probability density P(O, v) = P(O|v)P_V(v), assuming a gamma distribution for the marginal velocity distribution P_V(v). The equiprobability density contours approximately enclose 68%, 95%, and 99% of the joint probability. For small values of the residual intrinsic scatter σ_C, the conditional and joint distribution of the color and velocity are more asymmetric around the apparent mode (solid red line) and the intrinsic mean (solid blue line). Furthermore, the "blue edge" of the apparent color distribution is more squashed.