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Unformatted text preview: F(y) = 1θ y 0<y<1 = 0 elsewhere Where . a. Find the method of moment estimator of . Solution: 1 ) ( 1 + = = ∫ dy y Y E . Therefore: Y Y Y= ⇒ + = 1 ˆ 1 b. Show that Y is a consistent estimator of 1 + . Solution: 1 ) ( ) ( + = = θ Y E Y E ∞ → = ⇒ = n Y V n Y V Y V as ) ( lim ) ( ) ( 5. Y i are independent, identically distributed from a normal distribution. In our sample we find n = 20; 9 = Y , S 2 =43.158 a. Construct a 95% confidence interval for the mean. Solution: S =6.57. 95% CI is: n S t Y 19 025 . ± 9 ± 2.093 (6.57/√20) 9 ± 3.0748 [5.93, 12.07] b. Construct a 90% confidence interval for σ 2 . Solution: 117 . 10 , 1431 . 30 2 95 . 2 05 . = = χ 90% CI is [ ] 117 . 10 ) 158 . 43 )( 19 ( , 1435 . 30 ) 158 . 43 )( 19 ( [27.2, 81.05] 2...
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This note was uploaded on 04/13/2011 for the course ECON 506 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Staff

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