Question 2. Suppose Y₁, Y2,,YN is a random sample from a population with mean and variance o². Rather than using all N observations, consider an easy estimator of that uses only the first two observations Y* = Y₁ + Y2 2 (1) Show that Y* is a linear estimator. (2) Show that Y* is an unbiased estimator. (3) Find the variance of Y*.

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Question 2. Suppose Y₁, Y2,, YN is a random sample from a population with mean
variance o². Rather than using all N observations, consider an easy estimator of that uses
only the first two observations
Y* =
Y₁ + Y2
2
(1) Show that Y* is a linear estimator.
(2) Show that Y* is an unbiased estimator.
(3) Find the variance of Y*.
(4) Explain why the sample mean of all N observations is a better estimator than Y*.
Transcribed Image Text:and Question 2. Suppose Y₁, Y2,, YN is a random sample from a population with mean variance o². Rather than using all N observations, consider an easy estimator of that uses only the first two observations Y* = Y₁ + Y2 2 (1) Show that Y* is a linear estimator. (2) Show that Y* is an unbiased estimator. (3) Find the variance of Y*. (4) Explain why the sample mean of all N observations is a better estimator than Y*.
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