Hi guys

I'm trying to solve this

I have this pdf

I must find the maximum likelihood estimator of the expected value

I did this

The log of the last expression is

In its derivative the disappears

Without taking the log I end maximizing the same expression (the exponent of )

How can I proceed?

I see that I can express the pdf in this way:

This is the exponential distribution multiplied by a constant (but i know that it is defined for different values of x)

Is this a wrong path?

Thanks!