# Question

Let X = [X1, X2, X3] T represent a three- dimensional vector of random variables that is uniformly distributed over a cubical region

(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).

(e) Are the Xi independent?

(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).

(e) Are the Xi independent?

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