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Unformatted text preview: 2 3. Let X, Y and Z be three independent random variables distributed as (i = X, Y, Z). By taking functions (i.e., sums, differences, products, ratios, etc.) of these random variables, construct new random variables with the following distributions. (5) (a) N(0, 1) (5) (b) (5) (c) t 2 (5) (d) F 1,1 (5) (e) Cauchy 4. Consider a random sample of size T = 16 from a N( 2 , 11.25) distribution. Assume your prior beliefs are 2N( , 11.25/ ), where = 1 and = 9. Finally, suppose the realized sample mean is = .25. (10) (a) Find the posterior density f( 2 * y). (10) (b) Find P( 2 > 0 * y). (10) (c) Find a .95 HPD interval for 2 . (10) (d) Consider the hypotheses H 1 : 2 # 1 and H 2 : 2 > 1. Find the posterior odds P(H 2 * y)/P(H 1 * y). 3 4...
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 Fall '08
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 Econometrics

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