## Combining relative errors

Hi,

I'm getting confused in combining relative errors.
I have a relative error in evaluating the energy of some particle which is due to a wrong location of the spectrogram centre. this errors affects the energy and the relative error due to the energy resolution of the system.
Thus I have two relative errors: the one due to the centre location and the one due to the resolution which are actually dependet.

How I have to combine both errors? is it correct to sum them?
 Recognitions: Science Advisor So long as two errors are independent, the total error is square root of sum of the squares of errors. = + <(X+Y)²> = + + 2 Square of the error is the variance, which is defined Var(X) = -² Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y) Where covariance, Cov(X,Y) = - and is zero for independent X and Y.
 You are absolutely right, but the thing is that I don't think the errors are not indipendent: the error in the energy due to the wrong centre location affects the error due to the intrinsic resolution of the system...

Recognitions: