Question: =+20.26. Construct in R& a random variable X that is uniformly distributed over the surface of the unit sphere in the sense that |X| =

=+20.26. Construct in R& a random variable X that is uniformly distributed over the surface of the unit sphere in the sense that |X| = 1 and UX has the same distribution as X for orthogonal transformations U. Hint: Let Z be uniformly distributed in the unit ball in R4, define v(x) =x/|x| (4(0) =(1,0 ,..., 0), say), and take X = ₲(Z).

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