# Question

Let represent a three- dimensional vector of random variables that is uniformly distributed over the unit sphere. That is,

(a) Find the constant c.

(b) Find the marginal PDF for a subset of two of the three random variables. For example, find f x1, x2 (x1, x2).

(c) Find the marginal PDF for one of the three random variables. That is, find fX1 (x1).

(d) Find the conditional PDFs fX1|X2, X3 (x1|x2, x3) and fX1|X2, X3 (x1|x2, x3).

Extra: Can you extend this problem to - dimensions?

(a) Find the constant c.

(b) Find the marginal PDF for a subset of two of the three random variables. For example, find f x1, x2 (x1, x2).

(c) Find the marginal PDF for one of the three random variables. That is, find fX1 (x1).

(d) Find the conditional PDFs fX1|X2, X3 (x1|x2, x3) and fX1|X2, X3 (x1|x2, x3).

Extra: Can you extend this problem to - dimensions?

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