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
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53306e4a-5518-4d59-9324-b77d5eb8fc19%2F285ea7ea-96ca-4bed-b939-f927350baaab%2Fnp64ycg_processed.png&w=3840&q=75)
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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