Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 $\Theta$

Any help would be highly appreciated. Please help me!

share|improve this question
4  
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. If this is homework, please add the homework tag; people will still help, so don't worry. Please consider rewriting your post. –  Did Dec 13 '12 at 19:32
    
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
1  
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

1 Answer 1

\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.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.