Please answer step by step Sampling distributionSampling distributionof 0₂of ₁A0ÔThe above shows the sampling distributions of the two alternative estimators ₁ and 2 for the population parameter 0.Which statement is incorrect?Select one:O a. On average, both estimators have the mean value equal to in repeated samplingO b. 1 should be preferred it is more efficient with a larger variabilityO C.Both estimators are unbiasedO d. 2 should be preferred because it is more efficient with a lower variability

Answered: Sampling distribution Sampling…

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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Question

Please answer step by step

Sampling distribution
Sampling distribution
of 0₂
of ₁
A
0
Ô
The above shows the sampling distributions of the two alternative estimators ₁ and 2 for the population parameter 0.
Which statement is incorrect?
Select one:
O a. On average, both estimators have the mean value equal to in repeated sampling
O b. 1 should be preferred it is more efficient with a larger variability
O C.
Both estimators are unbiased
O d. 2 should be preferred because it is more efficient with a lower variability

Expert Solution

Step 1

Given:

The given information is the sampling distribution of the two alternative estimators for ${\hat{θ}}_{1} a n d {\hat{θ}}_{2}$ for the population parameter $θ$ .

Definition of efficient estimator:

An efficient estimator is defined as a minimum variation or minimum mean square error, it indicates that there is less difference between the estimated value and the true value.

Definition of kurtosis.

Kurtosis is a measure of the peakedness of the data.

Definition of Unbiased:

An estimator is said to be unbiased if

$E (T) = θ W h e r e T i s e s t i m a t o t a n d θ i s t h e p a r a m e t e r .$