# Sufficient statistic and MLE problem

Let $X_1, \ldots, X_n$ be i.i.d. random variables with pdf $\Theta x^{-2}$, $0 < \Theta \leq x < \infty$.

1. Find a sufficient statistic for $\Theta$.
2. Find the MLE of $\Theta$

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I have flagged this question for moderator attention due to the repeated vandalism. –  cardinal Dec 16 '12 at 17:44
Sorry for this... I really want delete the posts... –  wawataiji Dec 16 '12 at 17:45
BUt I can't the delete the button... –  wawataiji Dec 16 '12 at 17:46
As cardinal said, you cannot delete a question with upvoted answers. People have devoted time to giving good answers to your question; it would be unfair to them to simply delete your question. People might remove their downvotes if you explain how you encountered the problem, what you have tried, and what is causing you difficulty. –  robjohn Dec 16 '12 at 18:13

\begin{align} \hat{\theta}&=\displaystyle \arg\max_\theta L(\theta,X)\\ \hat{\theta}&=\displaystyle \arg\max_\theta \quad \theta^n\, \Pi_i^n X_i^{-2} \end{align} Clearly, you should increase $\hat \theta$ to increase the likelihood. But you can't really do that. Why? (Think about how the relation between $\theta$ and x is defined).

Figure this out and you (almost) have your sufficient statistic.

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