at some point during calculation the formula of the sum of the expected value becomes a single expected value:
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:
- What does the expectation of a value mean, in this case what is even $E[X_n]$
- Why should the expected value of an observation value be equal?
- 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