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If i'm using this method to generate points inside a sphere with radius K:

X = S^(1/3)*sqrt(1-V^2)*sin(O)

Y = S^(1/3)*V

Z = -S^(1/3)*sqrt(1-V^2)*cos(O)

where (0 < s < K^3), (-1 < v < 1) and (0 < o < 2*pi), i guess that:

S_PDF(s) = 1/(K^3)

V_PDF(v) = 1/2

O_PDF(o) = 1/(2*pi)

How come the joint distribution of S, V and O is 1/(4*pi*K^3)?

Shouldn't it be 1/(4*pi*K^3/3) because the volume of the sphere is 4*pi*K^3/3?

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# I Sphere probability

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