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Unformatted text preview: has a standardized Cauchy distribution. 3. Suppose X and Y have the joint p.d.f. f(x, y) = exp(-y), for 0 < x < y < 4 , and zero elsewhere. (5) (a) Are X and Y independent? (20) (b) Find Prob(X + Y < 1). 2 4. Let X denote consumption. Consider the constant relative risk aversion (CRRA) utility function Assume " 1. (10) (a) Let Z = R n(X). Denote its p.d.f. by f Z (z) = exp(z)f X [exp(z)] and its moment generating function by M Z (t) = E Z [exp(tZ)]. Assume M Z (t) exists at t = 1 - " . Express expected utility in terms of M Z ( @ ). (10) (b) Suppose Z -N( : , F 2 ). Find E[U(X)]. (5) (c) Suppose Z -t( 2 , * 2 , < ), where 0 < < < 4 . Find E[U(X)]....
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- Fall '10