# Is threre a relation between relative or absolute error and standard deviation for ratio of power spectra?

I have to compute the variance on this ratio, that is to say on the observable $$O$$ :

$$O=\left(\frac{C_{\ell, \mathrm{gal}, \mathrm{sp}}^{\prime}}{C_{\ell, \mathrm{gal}, \mathrm{ph}}^{\prime}}\right)=\left(\frac{b_{s p}}{b_{p h}}\right)^{2}\quad(1)$$

where $$C'_{\ell}$$ are angular power spectra (or matter power spectra).

Can I apply for this the computation of relative or absolute error like in electricity, we have $$U=RI$$ and the error on the quantity $$R$$ :

$$\dfrac{\Delta R}{R}= \dfrac{\Delta U}{U}+\dfrac{\Delta I}{I}$$

Is there a relation between absolute or relative error with the standard deviation of theses ratio ?

I would like to apply it to equation($$1$$) to compute this error or variance : is the right method ? If not, which solution would be possible ?

I have difficulties to grasp the subtilities between uncertainty and standard deviation : I just need to compute $$\sigma_{o}^{2}$$.