Addition of signal variance and noise variance Can I add two variances directly? I have my noise variance $\sigma_{noise}=-10 \ \mathrm{dB}$ and signal variance, $\sigma_{signal}=40 \ \mathrm{dB}$. So, can I say the total variance is $\sigma_{total}=30 \ \mathrm{dB}$?

I will use this total variance to generate random variables using a normal distribution with $\mu =0$ and $\sigma = \sigma_{total}$.
If the signal and noise are uncorrelated then the variance of the sum of the two equals the sum of their variances. So, yes, you can add variances (of uncorrelated signals). However, you cannot add dB-values! First of all, a variance in dB does not make sense because dB quantifies the ratio between two values. What you probably mean is dBm or dBW. So before adding variances you have to compute their actual (linear) values from the given values in dB(m/W).