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1) What property do we want to be true to make sure 0 is an unbiased estimator of O? O E(6) – 0 = 0 O E (6) – 0 + 0 %3D O E(0) – ô = 0 O None of them O E(0) – ô ± 0 2) How should we define S? to make sure that it is an unbiased estimator of o? (zi – 2)² O None of them (Tị – 7) n -

1) What property do we want to be true to make sure 0 is an unbiased estimator of O? O E(6) – 0 = 0 O E (6) – 0 + 0 %3D O E(0) – ô = 0 O None of them O E(0) – ô ± 0 2) How should we define S? to make sure that it is an unbiased estimator of o? (zi – 2)² O None of them (Tị – 7) n -

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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1) What property do we want to be true to make sure \(\hat{\theta}\) is an unbiased estimator of \(\theta\)? - \( \circ \) \(E(\hat{\theta}) - \theta = 0\) - \( \circ \) \(E(\hat{\theta}) - \theta \neq 0\) - \( \circ \) \(E(\theta) - \hat{\theta} = 0\) - \( \circ \) \(E(\theta) - \hat{\theta} \neq 0\) - \( \circ \) None of them 2) How should we define \(S^2\) to make sure that it is an unbiased estimator of \(\sigma^2\)? - \( \circ \) \(\frac{1}{n-1} \sum_i (x_i - \bar{x})^2\) - \( \circ \) \(\frac{1}{n} \sum_i (x_i - \bar{x})^2\) - \( \circ \) \(\frac{1}{n} \sum_i (x_i - \bar{x})\) - \( \circ \) \(\frac{1}{n-1} \sum_i (x_i - \bar{x})\) - \( \circ \) None of them
Transcribed Image Text:1) What property do we want to be true to make sure \(\hat{\theta}\) is an unbiased estimator of \(\theta\)? - \( \circ \) \(E(\hat{\theta}) - \theta = 0\) - \( \circ \) \(E(\hat{\theta}) - \theta \neq 0\) - \( \circ \) \(E(\theta) - \hat{\theta} = 0\) - \( \circ \) \(E(\theta) - \hat{\theta} \neq 0\) - \( \circ \) None of them 2) How should we define \(S^2\) to make sure that it is an unbiased estimator of \(\sigma^2\)? - \( \circ \) \(\frac{1}{n-1} \sum_i (x_i - \bar{x})^2\) - \( \circ \) \(\frac{1}{n} \sum_i (x_i - \bar{x})^2\) - \( \circ \) \(\frac{1}{n} \sum_i (x_i - \bar{x})\) - \( \circ \) \(\frac{1}{n-1} \sum_i (x_i - \bar{x})\) - \( \circ \) None of them
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