Note: This month, because the question is wellknown, no Internet searching
whatsoever, please.
Let X_{1},...,X_{n} be independent random variables, all distributed uniformly in [a, b] for some unknown a and b. This month's question: find (with proof) the minimum variance unbiased estimator of the expectation of the n random variables. (Or prove it does not exist.) Some explanations regarding the terminology:

List of solvers:RaduAlexandru Todor (8 November 11:23)Jan Fricke (22 November 01:47) Bart De Vylder (24 November 19:40) 
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The solution will be published at the end of the month.
Enjoy!