Unformatted text preview: (c) Is it true that q ( ˆ θ Bayes ) = E ( q ( θ ) | x ) where ˆ θ Bayes is the Bayes posterior mean estimate of θ ? 3. Suppose that X 1 , . . . , X n is a sample from a population with density f ( x | θ ) = θx θ-1 , < x < 1 , θ > 1 so that each X i is beta( θ, 1). Let T ( ~ X ) =-1 n n X i =1 log X i . (a) Show E ( T ( ~ X )) = 1 /θ , and Var( T ( ~ X )) = 1 /nθ 2 . (You should not need a lot of calculations here!) 4. C & B 10.3, p.505 5. C & B 2.33 a-c; read page 62. 6. Use the expression for the MGF of the natural suﬃcient statistic of an exponential family to compute the MGF of the suﬃcient statistic when doing iid sampling from (a) binomial (b) Poisson....
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This note was uploaded on 12/14/2010 for the course ORIE 6700 taught by Professor Woodard during the Fall '10 term at Cornell.
- Fall '10