Differentiating the Normal dist wrt mu and sigma for MLE

[mcallist]

Hi there,
I'm looking at example 10.4 in the CMP for finding the MLE of Mu and sigma for the normal distribution.
I don't understand two parts and I was hoping that someone could please help.

Firstly, would it be possible to please see from first principles, how the first line of the solution is broken out. This is just how the likelihood is arrived at from multiplying the pdfs together. I don't get why the mu stays in the square inside the summation at the end of it.

Secondly, when the log Likelihood is differentiated wrt sigma, the mu stays in the answer.

Apologies if these are ridiculous questions. It would really help if someone could break it down step by step please.

Thanks v much.
Tom

 

[Bharti Singla]

Hope this helps!
Did you get differentiation w.r.t mu? If you have further any doubt in it, please ask.

 

[mcallist]

Thanks so much Bharti. Sorry about the late reply. That's incredibly helpful. Cheers

 

[Bharti Singla]

Thanks so much Bharti. Sorry about the late reply. That's incredibly helpful. Cheers

Pleasure!!