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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A Deriving the standard normal distribution

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**