Question: Evaluation of indexed variables in a Product(...) and `*`(...) commands

Hi everybody, 

I generate random variables of the form X__E__n, n=1..N where N is assigned to some integer value (the double index is not a crucial point for the issue already appears with a single level of index).
Next I want to express a likelihood based upon these random variables in two different ways : a very symbolic one which uses the function "Product" an a second one that uses "product".

My problem is that I can't obtain the desired expressions.
As "Product" returns me a completely satisfactory expression, "product" (as I use it) refuses to return me the desired expression.

Without doubt this is due to a poor knowledge of the detailed way Maple proceeds to evaluate indices in seq, sum or product.
All explanation will be largely appreciated.

Thanks in advance

Download WhatHappensHere.mw