finding the MLE

**chutiya** · February 24th 2011, 02:17 PM

I have a question about finding the MLE..

$Let\;\; $X_1, \cdots, X_n$ \mbox{be a random sample from a population with pdf}\;\;$f_{\theta}(x)=(\theta+1)x^{\theta}$
$;\;0<x<1;\;\mbox{where }\theta>-1$ \mbox{is an unknown parameter}.$

Find the MLE for $e^{\theta}$

I am confused on how to start this. To find the MLE of $\theta$ , we would find the likelihood function of $L(\theta|x)$ . so does this mean the to find the MLE for the MLE for $e^{\theta}$ , I would go like this:

$L(e^{\theta}|x)= \prod_{i=1}^n (e^{\theta}+1){x_i}^{e^{\theta}}$

is this right??

**harish21** · February 24th 2011, 03:13 PM

Are you familiar with the Invariance Property of the MLEs?

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