Uniform distribution on the n-sphere.

  • #1
MathematicalPhysicist
Gold Member
4,287
202

Main Question or Discussion Point

Hi, I have the next RV:

$$\underline{W}=\frac{\underline{X}}{\frac{||\underline{X}||}{\sqrt{n}}}$$
where $$X_i \tilde \ N(0,1)$$
It's a random vector, and I want to show that it has a uniform distribution on the n-sphere with radius $$\sqrt{n}$$.

I understand that it has this radius, just calculate it. But I don't understand from calculating the CDF how to I arrive at uniform distribution.

Thanks in advance, MP.
 

Answers and Replies

  • #2
mathman
Science Advisor
7,821
433
You need to convert to n dimensional spherical coordinates. The "area" distribution should be uniform.
 

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