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5. Suppose that Y₁, Y2, Y3 denote a random sample from an exponential distribution with density function f(y) = 1e-³, y>0, 0>0 Y₁+Y2, 03² Y₁ + 2Y₂ Five estimators are proposed for the parameter 0,0₁ = =Y₁, 0₂ = , Ô₁ = Y(1) = 2 3 and Ô5 = Y (a) Compute the bias of each estimator and hence identify the unbiased estimators.

5. Suppose that Y₁, Y2, Y3 denote a random sample from an exponential distribution with density function f(y) = 1e-³, y>0, 0>0 Y₁+Y2, 03² Y₁ + 2Y₂ Five estimators are proposed for the parameter 0,0₁ = =Y₁, 0₂ = , Ô₁ = Y(1) = 2 3 and Ô5 = Y (a) Compute the bias of each estimator and hence identify the unbiased estimators.

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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5. Suppose that Y₁, Y2, Y3 denote a random sample from an exponential distribution with density function 1 f(y) == e 6, y> 0, 00 Y₁ + 2Y₂ Five estimators are proposed for the parameter 0, Ô₁ = Y₁, 0₂: Y₁+Y₂ 03 2 = Ô₁ = Y(1) = " 3 and Ô5 = Y (a) Compute the bias of each estimator and hence identify the unbiased estimators. (b) Find for each of the estimators, the mean square error and hence the standard error. (c) Find the efficiency of 85 relative to each of the other four estimators and comment on your results.
Transcribed Image Text:5. Suppose that Y₁, Y2, Y3 denote a random sample from an exponential distribution with density function 1 f(y) == e 6, y> 0, 00 Y₁ + 2Y₂ Five estimators are proposed for the parameter 0, Ô₁ = Y₁, 0₂: Y₁+Y₂ 03 2 = Ô₁ = Y(1) = " 3 and Ô5 = Y (a) Compute the bias of each estimator and hence identify the unbiased estimators. (b) Find for each of the estimators, the mean square error and hence the standard error. (c) Find the efficiency of 85 relative to each of the other four estimators and comment on your results.
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