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Question 1 (20 points). Suppose that Yı, Y2, ..., Yn is an iid sample from a U(0,1) distribution. (a) Show that 6 = 27 – 1 is

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Answer #1

TOPIC:Unbiased estimator ,Standard error of an estimator.

iid sample from Question-4 Here, 81, 82, - In be v (0,0) - distr. So, pod of vis - 2/3) = Sto; 02181 o rotherwise. in E (Y)(1-0) (H0 +0) 2 3(1-0) - 5 (1+0+02) ! Var(Y) = E(72) - E24). = 3 (1+0+02) - [1402 = § (1+0+02 - (148) 2 4+40+40» – 3-68 - 302@ Dafinen s 5 - sampe man. so, E (9) = (* x:). .). 2 (100). (140 HO So, E(T) = 140. >> E (27) = 1+0. :) E (27-D=0. - Hence ,n (1-0)2 12 m2 - = (1-0) 2 12 ń So, we have, > V ( 6 ). = var (27) var (25). =22: van (T). 3n = 4. Van (5). = 4. Siche = 120© we have, E (Ô),=0. E (1-5) = 1-0. - 13 mm v3n Jan s So, I = is an unbiased is an unbiased estimaton of on; where, ô = (29-1

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