Another ASM Course 4 question

[Alien]

On page 43 of the ASM, why does one have to set lnf(x) = 0 in order to find the Variance (rather than asymtotic Variance) of the mle estimator. Thanks for your answer!

[Tri4Ben]

I believe that you use the log likelyhood instead of just the likelyhood to find the MLE because it can usually be solved in closed form. The function, f(x)=ln(x) has no extrema of its own so taking the log of something will not change it. This technique is also used in exam 1 when finding limits as x approaches 0. There is an example in the sample exam. Hopefully a professor will give you a better explanation soon.