(Steps Shown) If X_1, X_2, ..., X_n is a random sample from a distribution with pdf f(x ; θ)


Question: If \(X_{1}, X_{2}, \ldots, X_{n}\) is a random sample from a distribution with pdf

\[f(x ; \theta) = \left\{\begin{aligned} \frac{3 \theta^{3}}{(x+\theta)^{4}}, & 0 Show that \(Y=2 \bar{X}\) is an unbiased estimator of \(\theta\) and determine its efficiency.

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