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## Homework Statement

Hi guys!

I have solved a log-likelihood problem and its Newton-Raphson Iteration. My step-by-step solution is attached.

The only problem I have is when I plug in numbers, the final number for the first order Newton-Raphson is different from my professor's.

I guess you don't need any numbers. If you can can detect a mistake in my formula derivation, I will really appreciate it.