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Find the MLE

So for this question how would you go about finding the MLE? because finding the derivative of the log likelihood gives you a zero. How would I go about solving this question?

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    $\begingroup$ What is the maximal $\theta$ such that $X_i\ge \theta$ for all $i=1,\dots, n$? $\endgroup$ – d.k.o. Apr 16 '16 at 3:21
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    $\begingroup$ would that just be the min Xi? $\endgroup$ – Yeti Apr 16 '16 at 16:15

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