The sum of the dependent variable is
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The mean of the sum is the same as the sum of the mean even if the variables are dependent. So while Var(X+Y)=Var(X)+Var(Y) for independent variables, or even variables which are dependent but uncorrelated, the general formula is
Var(X+Y)=Var(X)+Var(Y)+2Cov(X,Y)
where Cov is the covariance of the variables.
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