I haven't run into any PE questions that have this problem, but I found this on Math SE: http://ift.tt/1sSsP2J .
One thing I know about
is that 
, where 
, so of course, 
. Thus, to maximize 
, do we choose 
?
What if the support of the
were 
? Then would there be NO MLE for ?
One thing I know about
is that , where , so of course, . Thus, to maximize , do we choose ?What if the support of the
were ? Then would there be NO MLE for ?MLE: what if l'(θ) is not a function of θ?
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