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Suppose Y₁, Y2,..., Yn is an iid sample from a beta (a, 3) distribution with a = 3 = 0,0 >0 a. Use the Factorization Theorem to show that n T = ∙ II Y¿(¹ — Y;) i=1 is a sufficient statistic.

Suppose Y₁, Y2,..., Yn is an iid sample from a beta (a, 3) distribution with a = 3 = 0,0 >0 a. Use the Factorization Theorem to show that n T = ∙ II Y¿(¹ — Y;) i=1 is a sufficient statistic.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 8E
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Suppose Y₁, Y2,…, Yn is an iid sample from a beta (a, ß) distribution with a = ß = 0, 0 > 0 a. Use the Factorization Theorem to show that n T = []Y;(1 — Y;) i=1 is a sufficient statistic. b. The sample variance n 1 = ΣΥ; - Y)2 n 1 i=1 is an unbiased estimator of the population variance 1 4(20 + 1)* Is S² the MVUE of o2? Explain.
Transcribed Image Text:Suppose Y₁, Y2,…, Yn is an iid sample from a beta (a, ß) distribution with a = ß = 0, 0 > 0 a. Use the Factorization Theorem to show that n T = []Y;(1 — Y;) i=1 is a sufficient statistic. b. The sample variance n 1 = ΣΥ; - Y)2 n 1 i=1 is an unbiased estimator of the population variance 1 4(20 + 1)* Is S² the MVUE of o2? Explain.
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