From:

TUTOR@teluq.ca
Date: AUGUST 2024

Subject: RE: INF1421 module 3 start Case of univariate density

To: ME

Hello ME,

the partial derivative of the log-likelihood with respect to θ2 is obtained by differentiating each term of the log-likelihood with respect to θ2, then combining the results. The condition for maximizing the log-likelihood gives us an equation to estimate θ2.

I have not found a clearer method than manual calculation.

I have attached the derivation that I did by hand, following the rules. I hope it will be easier for you to follow.

I apologize for my handwriting.

Do not hesitate to let me know if you have any further questions.

Best regards,

TUTOR

From: ME

Sent: AUGUST 2024

To:

TUTOR@teluq.ca
Subject: INF1421 module 3 start Case of univariate density

Hello TUTOR,

I am writing to you regarding the 3rd module of INF1421, specifically the start of the subsection Case of univariate density of section 3.2.3, on page 6. I am having difficulty understanding how we arrive at the derivative, i.e. from the 1st formula of

to the 2nd. Regarding the 1st element of the matrix, how come we have to keep 1 / θ˅2 but have to discard the rest of the fraction, i.e. the -1/2. Regarding the 2nd element of the matrix, where does the square (exponent 2) of the denominator of the 2nd part come from? Could you refer me to a page of a free site or a free document to better understand?

There are several pages left in the module so I might contact you again for that.

Thank you,

ME