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lets say $Y_{1},\ldots,Y_{n}$ are simple random samples with the PDF: $f_{\theta}(y)=\theta y^{\theta - 1} \mathbb{I}(0 \le y \le 1) $
How can I find the PDF of $\bar{Y}$? is it even possible?

Abdallah Barghouti
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    Exact distribution for any $n$ likely does not have a closed form pdf. Why do you need it? – StubbornAtom Apr 05 '21 at 07:11
  • I want to find $E(\frac{\bar{Y}}{1 - \bar{Y}})$ and the only way I thought of is to find the PDF of $\bar{Y}$ and then to compute by the definition – Abdallah Barghouti Apr 05 '21 at 07:19
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    Previously asked: https://stats.stackexchange.com/q/202432/119261. I guess the original problem is to check if the MOM estimator $\frac{\overline Y}{1-\overline Y}$ is unbiased for $\theta$ or not. If that is the case, then you don't need to find the exact expectation: https://math.stackexchange.com/q/3185959/321264. – StubbornAtom Apr 05 '21 at 07:27
  • @StubbornAtom thanks :) – Abdallah Barghouti Apr 05 '21 at 07:38

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