(a) Show that T₁ is an unbiased estimator of 1/A. (b) Find the constant a such that T₂ = aX(1) is an unbiased estimator of 1/X. (c) Since T₁ and T₂ are both unbiased we prefer the estimator with smaller variance. Which of the estimators T₁ and T₂ would you choose for estimating the mean 1/X?
(a) Show that T₁ is an unbiased estimator of 1/A. (b) Find the constant a such that T₂ = aX(1) is an unbiased estimator of 1/X. (c) Since T₁ and T₂ are both unbiased we prefer the estimator with smaller variance. Which of the estimators T₁ and T₂ would you choose for estimating the mean 1/X?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![1. Suppose we have a random sample X₁, X2, ..., Xn from an Exponential distribution with mean
1/A. Suppose we want to estimate the mean 1/A. One estimator for 1/X is T₁ = X. Of interest
is to note that the minimum of X₁, X2,..., Xn, say X(1), has an Exponential distribution with
mean (n)-¹.
(a) Show that T₁ is an unbiased estimator of 1/A.
(b) Find the constant a such that T₂ = aX(1) is an unbiased estimator of 1/X.
(c) Since T₁ and T₂ are both unbiased we prefer the estimator with smaller variance. Which
of the estimators T₁ and T₂ would you choose for estimating the mean 1/X?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53868a16-d184-436d-8ec4-11c77bbeac21%2F2ca4d98a-fc84-48cf-81a5-4d6897c161ef%2Fiuer8nq_processed.png&w=3840&q=75)
Transcribed Image Text:1. Suppose we have a random sample X₁, X2, ..., Xn from an Exponential distribution with mean
1/A. Suppose we want to estimate the mean 1/A. One estimator for 1/X is T₁ = X. Of interest
is to note that the minimum of X₁, X2,..., Xn, say X(1), has an Exponential distribution with
mean (n)-¹.
(a) Show that T₁ is an unbiased estimator of 1/A.
(b) Find the constant a such that T₂ = aX(1) is an unbiased estimator of 1/X.
(c) Since T₁ and T₂ are both unbiased we prefer the estimator with smaller variance. Which
of the estimators T₁ and T₂ would you choose for estimating the mean 1/X?
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