Maximum Likelihood estimators of population mean and variance - part 1

In this video I explain how Maximum Likelihood Estimators of the population mean and variance can be derived, under the assumption of a normal error term in the population.

[negarabbaspourmani]

Amazingly explained videos! I can't thank you enough for making it easier for me to undestand econometrics :)

[eswariebalan]

These videos are amazing -provides clear and concise understandof the topic at hand - better than the Green, Hanse or Hayashi texts

[iisimik]

Thanks, man. You've helped me a lot.

[lastua]

Why could he take out 1/2sigma_sq at 5:48 when he had to add a power N to the initial term to take it out of the product operator?
Why could we replace the product operator with a summation operator then (considering the first question)?

[ainulhusnabintijamaludin]

why at 4:48 there's no log for n*1/sqrt 2pi sigma^2?

[madhurasutar]

Does max likehood give minimum variance unbiased estimator?

[connorgower]

I don't understand near the beginning where you said ei =  xi - (mu) - how can we use this in the probability for an observation of xi, when this is the probability of xi - mu ? Haven't we instead therefore found f( ei | mu, sigma^2) and not f( xi | mu, sigma^2) ? And as we know ei ~ N(0, sigma^2), surely we can plug in mu = 0 into the pdf for the normal distribution and simplify? Thanks anyway for all these videos though - they are great! :)

[ShethBhavik]

Do you mean ln(e^x) = x instead of log(e^x)=x at 5:13?

[lastua]

Did he forget a log operator in the last term?