It would help greatly if we had the context for this problem. It looks to me like some sort of least-squares fit (maybe log-likelihood?). Please define every single variable I see. That is, what are each of the following:
Do any of these variables depend on any of the others, aside from depending on and
Thanks for asking!
beta - is a modeling parameter
alfa - is chosen as the maximum likelihood estimate
LL - is the first equation (in square shape)
n - is the index of the numbers in the samle (from i - n)
mu(i) is the value of the element ( for example i = 3; mu(i)=254.2...etc)
This is a sample with some positive numbers. I'm asked to do this: Suppose you are free to choose both parameters alfa as well as beta . Can you derive
the MLE (maximum likelihood estimates) for both parameters simultaneously? I've got the derive fore alfa, but I'm stuck for beta. Is it more clear now? It's a long problem, this was the reason didn't want to post much info, just the equations. Thanks a lot!
So, more generally, you're asking if
I do not think it very difficult to convince yourself that this is false in general. Let a constant, and let Then the equation would have us believe that
or
which is certainly not true if say. The result is only true if in which case your summation really isn't doing anything, as there is only one term!
Does that clear things up?
I tried it with doing some test after I asked, and I concluded that it was a stupid question. I wanted to simplify some things through my equations, but when you are not able to do so, it's better not to invent formulas :PP
Thanks a lot!