Re: Uniform probability density on the unit circle

As the circumference is 2*pi, this is why I divide by 2*pi to get the
density. My problem remains.

Ray Koopman wrote:
Al wrote:
Hi,
can someone tell/explain me, what is the uniform probability density on
the unit circle?
I would say,
p(x,y)=1/(2*pi)*delta(x^2+y^2-1), where delta() is the delta
function.

But now, if I easily integrate it,
int(-1..1)int(-1..1) p(x,y) dx dy=int(-1..1)int(0..1) p(x,y) dx dy=...,
using the substitution z:=x^2+y^2-1,
the result is 0.5.
So, why isn't the total probability 1? Do I make a mistake in the
integration or is the assumed density incorrect by a factor of two?
Thanks for your help,
Al

Hint: area = pi*r^2, circumference = 2*pi*r

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