If i have two random variables X and Y, then $E[X+Y]=E[X]+E[Y]$ . However, do X and Y have to be independent ?
Do you know where i can find a proof of this principle ?
2026-04-12 13:30:57.1776000657
Expected Value of the sum of random variables
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No, they don't. This is called linearity of expectation and holds for all r.v's $X$ and $Y$ - in fact, it holds for a general sum of $n$ random variables regardless of any correlation.
If you google "linearity of expectation" there are lots of articles that have proofs in them