I've calculated the joint distribution, XY_PDF(x,y) of random(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# A Deriving the standard normal distribution

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