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Suppose Y₁, Y2,,Y,, is an iid sample from a beta (a, 3) distribution with a 3-0, 0>0 a. Use the Factorization Theorem to show that T-IIX(1-X) is a sufficient statistic. b. The sample variance 8²-1(1-P)² is an unbiased estimator of the population variance 4(20+1) Is S2 the MVUE of o2? Explain.

Suppose Y₁, Y2,,Y,, is an iid sample from a beta (a, 3) distribution with a 3-0, 0>0 a. Use the Factorization Theorem to show that T-IIX(1-X) is a sufficient statistic. b. The sample variance 8²-1(1-P)² is an unbiased estimator of the population variance 4(20+1) Is S2 the MVUE of o2? Explain.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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Suppose Y₁, Y2,,Y, is an iid sample from a beta (a, 3) distribution with a = 3=0,0>0 a. Use the Factorization Theorem to show that T-IIX(1-X) is a sufficient statistic. b. The sample variance S²-(X-P)² 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,,Y, is an iid sample from a beta (a, 3) distribution with a = 3=0,0>0 a. Use the Factorization Theorem to show that T-IIX(1-X) is a sufficient statistic. b. The sample variance S²-(X-P)² is an unbiased estimator of the population variance 1 4(20+1) Is S2 the MVUE of o2? Explain.
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