6.2.9. If X₁, X2,..., Xn is a random sample from a distribution with pdf 303 f(x; 0) (x+0)4 = -{ 0
6.2.9. If X₁, X2,..., Xn is a random sample from a distribution with pdf 303 f(x; 0) (x+0)4 = -{ 0
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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![(c) What is the asymptotic distribution of \(\sqrt{n}(\hat{\theta} - \theta)\)?
6.2.9. If \(X_1, X_2, \ldots, X_n\) is a random sample from a distribution with pdf
\[
f(x; \theta) =
\begin{cases}
\frac{3\theta^3}{(x+\theta)^4} & 0 < x < \infty, 0 < \theta < \infty \\
0 & \text{elsewhere}
\end{cases}
\]
Show that \(Y = 2\bar{X}\) is an unbiased estimator of \(\theta\) and determine its efficiency.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F718b1378-40e4-4c32-83bc-211fc46d7de4%2Fd78cf4a3-3fea-4555-b39f-538a40077138%2Fk9cbl0b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(c) What is the asymptotic distribution of \(\sqrt{n}(\hat{\theta} - \theta)\)?
6.2.9. If \(X_1, X_2, \ldots, X_n\) is a random sample from a distribution with pdf
\[
f(x; \theta) =
\begin{cases}
\frac{3\theta^3}{(x+\theta)^4} & 0 < x < \infty, 0 < \theta < \infty \\
0 & \text{elsewhere}
\end{cases}
\]
Show that \(Y = 2\bar{X}\) is an unbiased estimator of \(\theta\) and determine its efficiency.
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