How to show or prove that Y = 2X¯ is an unbiased estimator of θ and determine its efficiency?Please see attached mathematical statistics question. If $ X_1, \ldots, X_n $ is a random sample from a distribution with pdf\[f(x; \theta) = \begin{cases} \frac{3\theta^3}{(x+\theta)^4} & x \in \mathbb{R}^+, \theta \in \mathbb{R}^+ \\0 & \text{elsewhere}\end{cases}\]Show that $ Y = 2\bar{X} $ is an unbiased estimator of $ \theta $ and determine its efficiency.

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Answered: If X1,..., Xn is a random sample from a…

If X1,..., Xn is a random sample from a distribution with pdf 303 x E R+, 0 E R+ f(x; 0) = { (z+0)4 elsewhere Show that Y = 2X is an unbiased estimator of 0 and determine its efficiency.

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How to show or prove that Y = 2X¯ is an unbiased estimator of θ and determine its efficiency?

Please see attached mathematical statistics question.

If $ X_1, \ldots, X_n $ is a random sample from a distribution with pdf

\[
f(x; \theta) =
\begin{cases}
\frac{3\theta^3}{(x+\theta)^4} & x \in \mathbb{R}^+, \theta \in \mathbb{R}^+ \\
0 & \text{elsewhere}
\end{cases}
\]

Show that $ Y = 2\bar{X} $ is an unbiased estimator of $ \theta $ and determine its efficiency.

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