Suppose that X and Y are independent standard normal random variables and let W = XY. 4. (i) What is the conditional distribution of W given that Y y? What is the moment %3D generating function of this conditional distribution? (ii) Show that the moment generating function of W is Vw (t) = 1. for It| < 1 V1-t2 (Hint: Condition on Y and use the moment generating function of the variable from (i))

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