I've calculated the joint distribution, XY_PDF(x,y) of random variables X and Y (both coming from a distribution N(n) = C*e^(-K*n^2)). I use XY_PDF(x,y) to calculate the joint distribution AR_PDF(a,r) of the random variables A (angle) and R (radius), with the PDF method and the Jacobian. Since AR_PDF(a,r) = A_PDF(a)*R_PDF(r) and I want A_PDF(a) = 1/(2*pi), I can find that C = 1/(2*pi)^(1/2) in N(n), since the other factors in AR_PDF(a,r) calculated from XY_PDF(x,y) are related to R. If I do the same in 3D (using the longitude/latitude/radius distributions for producing a uniform surface distribution), I get C = 1/(2*pi)^(1/3) after discarding the factors related to the longitude distribution and the radius distribution. The correct answer (for a multivariate gaussian) should be 1/(2*pi)^(1/2) here also, right? Is my reasoning to find this constant C wrong? Is there a better way?