I am studying statistics, and it it, we are given many different results about what kind of estimations we can make and what kind of distributions these estimations have.
For example, assume $Y_1,\ldots,Y_n$ er iid normally distributed with some mean and variance…. then our estimation of the mean is the average, and this average is the realisation of a random variable which itself is normally distributed which mean $ = \mu$ and variance $= \sigma^2/n$.
But our book has no proof of this, and it's not part of the course, yet I'd like to know it anyways, but I have some trouble finding proofs of this on the internet. Does any of you know of certain sites where the proofs are given?
Every proof regarding a first year course in statistics, and proof for the theory of normal distributions especially, will work.
Best Answer
If I understand you question correctly this Wikipedia page will give a better explanation than what I can put into the post. (ie the sum of normally distributed random variables)
If you want to know where they come from, or at least there importance, I'd recommend getting your head around central limit theorem.