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Let X₁, X2, X3,..., Xn denote a random sample of size n from the population distributed with the following probability density function: e) f) g) where k> 0 is a constant. f(x; λ) = 2-kxk-1e (k-1)! 0, if x > 0 elsewhere Justify whether or not  is a uniform minimum variance unbiased estimator of λ. Check whether or not the MLE of λ is a consistent. Suggest with a Fisher's factorization theorem, the sufficient estimator of 1.

Let X₁, X2, X3,..., Xn denote a random sample of size n from the population distributed with the following probability density function: e) f) g) where k> 0 is a constant. f(x; λ) = 2-kxk-1e (k-1)! 0, if x > 0 elsewhere Justify whether or not  is a uniform minimum variance unbiased estimator of λ. Check whether or not the MLE of λ is a consistent. Suggest with a Fisher's factorization theorem, the sufficient estimator of 1.

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.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 7CR
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Let X₁, X2, X3,..., Xn denote a random sample of size n from the population distributed with the following probability density function: I e) f) g) where k> 0 is a constant. f(x; 2) = 2-kxk-1e (k-1)! if x > 0 elsewhere " Justify whether or not  is a uniform minimum variance unbiased estimator of 1. Check whether or not the MLE of λ is a consistent. Suggest with a Fisher's factorization theorem, the sufficient estimator of 1.
Transcribed Image Text:Let X₁, X2, X3,..., Xn denote a random sample of size n from the population distributed with the following probability density function: I e) f) g) where k> 0 is a constant. f(x; 2) = 2-kxk-1e (k-1)! if x > 0 elsewhere " Justify whether or not  is a uniform minimum variance unbiased estimator of 1. Check whether or not the MLE of λ is a consistent. Suggest with a Fisher's factorization theorem, the sufficient estimator of 1.
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