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(b) Let {X₁, X2,..., Xn] be a random sample from the probability distribution with probability density function: f(x; 0) = 8-1 for 20 0 is an unknown parameter. i. Derive the method of moments estimator of 8. ii. Is the estimator of 6 derived in part i. biased or unbiased? Justify your answer. Hint: You may use the fact that. E(X) = E(X). iii. Given that the variance of the method of moments estimator of @ in part. i. is 02/(27n), check whether the estimator is a consistent estimator of 8.

(b) Let {X₁, X2,..., Xn] be a random sample from the probability distribution with probability density function: f(x; 0) = 8-1 for 20 0 is an unknown parameter. i. Derive the method of moments estimator of 8. ii. Is the estimator of 6 derived in part i. biased or unbiased? Justify your answer. Hint: You may use the fact that. E(X) = E(X). iii. Given that the variance of the method of moments estimator of @ in part. i. is 02/(27n), check whether the estimator is a consistent estimator of 8.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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(b) Let (X₁, X2,..., Xn] be a random sample from the probability distribution with probability density function: Jo-¹ for 20 < x < -0 BIH f(x; 0) = otherwise where > 0 is an unknown parameter. i. Derive the method of moments estimator of 8. ii. Is the estimator of 9 derived in part i. biased or unbiased? Justify your answer. Hint: You may use the fact that E(X) = E(X). t iii. Given that the variance of the method of moments estimator of 0 in part. i. is 02/(27n), check whether the estimator is a consistent estimator of 0.
Transcribed Image Text:(b) Let (X₁, X2,..., Xn] be a random sample from the probability distribution with probability density function: Jo-¹ for 20 < x < -0 BIH f(x; 0) = otherwise where > 0 is an unknown parameter. i. Derive the method of moments estimator of 8. ii. Is the estimator of 9 derived in part i. biased or unbiased? Justify your answer. Hint: You may use the fact that E(X) = E(X). t iii. Given that the variance of the method of moments estimator of 0 in part. i. is 02/(27n), check whether the estimator is a consistent estimator of 0.
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