Let X1....X10 be a random sample from a distribution with the probability density function \(\rm f(x|θ)=\left\{\begin{matrix}θ x^{θ-1}, & if \:0
where θ > 0 Is an unknown parameter. The prior distribution of θ is given by
\(\rm \pi (θ)=\left\{\begin{matrix}θ e^{-θ}, & if\ θ>0\\\ 0, & otherwise,\end{matrix}\right.\)
The Bayes estimator of θ under squared error loss is
1
\(\rm \frac{12}{1-\Sigma_{i=1}^{10}ln X_i}\)
2
\(\rm \frac{11}{2-\Sigma_{i=1}^{10}ln X_i}\)
3
\(\rm \frac{3+\Sigma_{i=1}^{10}ln X_i}{13}\)
4
\(\rm \frac{2+\Sigma_{i=1}^{10}ln X_i}{11}\)