There are two methods to estimate the asymptotic distribution of mu( transition rate ) 1) differentiating integral, which is horrible 2) MLE method. Which one is the important in the view of exam?
I had concentrated more on the MLE method, although they haven't mentioned whether the other method should be done or not. I haven't seen any past question which asked us to derive the estimator using the first method. They have asked the MLE method derivation though. Can't comment on the importance as they haven't emphasized the same of either of the methods. But looking at the past exam questions, MLE method seems sufficient. Also, in the course notes, the MLE method is extended to the multiple state Markov Jump Process in Chapter 5, but the first method hasn't been extended in the same way.
Why in the asymptotic distribution of mu by central limit theorem the distribution of the given term (D-muV)/N has variance E (D)/N^2 and not E (D)/N? As we had assumed the N lives were iid so var of n iid lives will be n times the var of any individual? Which must lead to var of the term= E (D)/N
