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3. Suppose that X₁, X2, ..., Xn is a random sample from an exponential distribution with the probability density function f(x; ß) = ½e-¹/³, for x > 0 and some ß3 > 0. (a) Find the lower bound of the Cramer-Rao inequality for the variance of an unbiased estimator of 3. i.e., nI(3) · (b) Find an approximate 100(1 - a)% confidence interval for 3. Justify your answer by providing the appropriate theorem.

3. Suppose that X₁, X2, ..., Xn is a random sample from an exponential distribution with the probability density function f(x; ß) = ½e-¹/³, for x > 0 and some ß3 > 0. (a) Find the lower bound of the Cramer-Rao inequality for the variance of an unbiased estimator of 3. i.e., nI(3) · (b) Find an approximate 100(1 - a)% confidence interval for 3. Justify your answer by providing the appropriate theorem.

MATLAB: An Introduction with Applications
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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3. Suppose that X₁, X2, ..., Xn is a random sample from an exponential distribution with the probability density function f(x; ß) = ½e-¹/³, for x > 0 and some ß3 > 0. (a) Find the lower bound of the Cramer-Rao inequality for the variance of an unbiased estimator of 3. i.e., nI(3) · (b) Find an approximate 100(1 - a)% confidence interval for 3. Justify your answer by providing the appropriate theorem.
Transcribed Image Text:3. Suppose that X₁, X2, ..., Xn is a random sample from an exponential distribution with the probability density function f(x; ß) = ½e-¹/³, for x > 0 and some ß3 > 0. (a) Find the lower bound of the Cramer-Rao inequality for the variance of an unbiased estimator of 3. i.e., nI(3) · (b) Find an approximate 100(1 - a)% confidence interval for 3. Justify your answer by providing the appropriate theorem.
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