Let X, Y, Z be r.v.s such that X N (0, 1) and conditional on X = x, Y and Z are i.i.d. N
Chapter 7, Problem 11(choose chapter or problem)
Let X, Y, Z be r.v.s such that X N (0, 1) and conditional on X = x, Y and Z are i.i.d. N (x, 1). (a) Find the joint PDF of X, Y, Z. (b) By definition, Y and Z are conditionally independent given X. Discuss intuitively whether or not Y and Z are also unconditionally independent. (c) Find the joint PDF of Y and Z. You can leave your answer as an integral, though the integral can be done with some algebra (such as completing the square) and facts about the Normal distribution.
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