finding UMVUE of parameter $\displaystyle 3^{-\theta}$ [closed]

suppose $X_1,X_2,\ldots,X_n$ is a random sample of $Beta(\theta+1,1)$. how can find UMVUE of parameter $\displaystyle 3^{-\theta}$

closed as off-topic by Did, Dario, Najib Idrissi, Davide Giraudo, Claude LeiboviciFeb 22 '15 at 10:33

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, Dario, Najib Idrissi, Davide Giraudo, Claude Leibovici
If this question can be reworded to fit the rules in the help center, please edit the question.

Let $a$ in $(0,1)$, then $T=\mathbf 1_{X_1\lt a}$ is such that $\mathbb E_\theta(T)=a\cdot a^\theta$. Since $U=X_1\cdots X_n$ is a complete sufficient statistic, the unique UMVUE for $a^\theta$ is $S=a^{-1}\mathbb E_\theta(T\mid U)=a^{-1}\mathbb P_\theta(X_1\lt a\mid U)$.