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1. C & B 7.9, p.356. The Method of Moments estimator is 2; just take this as given, dont derive. x iid Also, you may use the following fact. If Yi f (x) for some density function f , then the density of maxi=1,.,n Yi has the
1. Prove that if T (X ) is a sucient statistic for , then the posterior density for depends on x only through T (x).
2. Suppose S is an unbiased estimator of and b = 0. Why is S + b inadmissible?
3. C & B 7.6 (a)-(b) on p. 35
1. Consider an experiment in which, for given , the outcome X has density f (x|) = 2x/2 , Let be a prior density for . (a) Find the posterior density of when () = 1, (b) Find the posterior density of when () = 32 , (c) Find E
(+ ) 1. The Beta density for x [0, 1] is given by f (x|, ) = ()( ) x1 (1 x) 1 where is the gamma function and , > 0 are the parameters. Write this density in exponential family form (which proves that it is a member of this f
ORIE 6700 MIDTERM, FALL 2010
Rules: Use only class notes and the one and only course text. You must work on your own without collaborating. Giving help is as serious a form of cheating as requesting help. (1) Let X1 , . . . , Xn be a random sample from f