If I have 3 random varibles X, Y and Z and X=Y+Z then var(X)=var(Y)+var(Z), but Y=X-Z therefore var(Y)=var(X)+var(Z), it is clear that these two contridict, so what makes one of them right and the other wrong? Thanks.
2026-03-27 17:04:57.1774631097
Variences and adding them from independent random variables?
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Your second version is wrong because random variables do NOT obey normal algebra: Since $X = Y + Z$, $X$ is perfectly correlated with both $Y$ and $Z$, hence the second formula, which treats $X$ as independent of the other two variables, is incorrect.