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For a sample of size n from a random variable with density function $$f_{\theta}(x)=\frac{2x}{\theta^2}, x>0$$

find the confidence interval for $\theta$ of average length consistently lower level of confidence $ 1 - \alpha $, based on a sufficient statistic.

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I apreciate any help, because i did not understand much exercise. –  Sophie Germain Jan 22 '13 at 18:16
    
You might have mis-transcribed the exercise, since the alleged density function isn't integrable over the indicated range. –  Andreas Blass Jan 22 '13 at 18:32
    
your density function is not integrable for x>0 however for this kind of question use properties of density function. im sure you can solve all problem (by tenacity and thinking ) –  Maisam Hedyelloo Jan 22 '13 at 18:40
    
Omg Sorry I am a silly -.- this isn't function –  Sophie Germain Jan 22 '13 at 18:41
    
You originally had $\dfrac{\theta}{x^2}$. My suspicion is that as a function of $x$, this is supposed to be a density on the interval $(\theta,\infty)$. –  Michael Hardy Jan 22 '13 at 21:15
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