Referring to: [How to understand that MLE of variance is biased in a Gaussian distribution](https://stats.stackexchange.com/questions/136673/how-to-understand-that-mle-of-variance-is-biased-in-a-gaussian-distribution/136703#136703?newreg=1531b7005bb642ff9d70e3d0bf00c2b1)

at some point during calculation the formula of the sum of the expected value becomes a single expected value:

[![confusing formula](https://i.stack.imgur.com/3eZbg.png)](https://i.stack.imgur.com/3eZbg.png)

The explanation given is:
With the last step following since due to $E[X^2\_n]$
being equal across n due to coming from the same distribution.

I can't understand:

1. What does the expectation of a value mean, in this case what is even $E[X\_n]$
2. Why should the expected value of an observation value be equal?
3. What's the proof for $Var[1/N \*...] = (1/N)^2 Var[...]$

Thanks for the help and sorry for the bad format I don't know how to write formulas, this is my first post xD