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Uniform distribution on the n-sphere.

  1. May 19, 2013 #1

    MathematicalPhysicist

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    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.
     
  2. jcsd
  3. May 20, 2013 #2

    mathman

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    You need to convert to n dimensional spherical coordinates. The "area" distribution should be uniform.
     
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