Cant get my head around gaussians, so easy aswell?

[physical101]

Hi there was wondering if some one could help me?
I think i understand what a gaussian is, its a normal distirbution where the distribution of data symmetrically tails off from the mean in both directions. I have been looking at FTIR error analysis and have constantly read that error is normally distributed. I have thought that this means that the majority of error introduced in the analysis is distributed around the mean.

I have also read that we should consider the distribution to stationary, and I have come to think of this as meaning that for for each signal the noise is independent.

My question is when viewing the normal distribution of error for stationary error points in books the mean is always zero.

Do i take this too mean that the mean is actually a stable error value and that the + and - points of inflection are deviations away from this stable value. So does this mean that in any normal distributions of error that the mean will always be 0?

So confused and would really appreciate it if any can help, i know its a bit basic for this site

thanks

 

[EnumaElish]

The mean error being zero is an assumption about the overall bias in a linear system: if y = A + B x + u and a and b are the estimated values for A and B (estimated from data), then E[y] = E[a] + E x + E. If E[a] = A (meaning a is an unbiased estimator of A), E = B (b is an unbiased estimator of B), and I want E[y] = y, then E = 0 has to be the case.

Stationarity means that E is not changing over time, so there's no upward or downward drift (in an expectational or distributional sense) between any two time periods.