Can you give me the equation for Gaussian distribution?
Can you give me it's log likelihood function?
Note: This is already given as part of the problem statement.
Can you show the detailed steps how you arrived at it?
Some paperwork
In the next slide we will solve for the below expression:
Some Logarithm Properties we would use:
Can you maximize the log likelihood expression w.r.t. mu and show the detailed steps?
Some paperwork for derivative of:
We will prove it next:
Some ‘Differentiation’ identities we would see next
And now maximize log likelihood w.r.t. sigma-squared and show the detailed steps
Identity:
References
https://chat.openai.com/share/4278db33-9b76-4d8b-9586-4e1e78844433
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