I know that Gauss-Markov process expected value is always zero but in normal distribution, mean can vary and Gauss-Markov process is a subtype of Gaussian process.
The reason behind this question is my homework. I have to find $E[y(x)]$ and $R_y[t_1,t_2]$ assuming $x(t)$ is Gaussian process. The transformation is linear: $y(t)=t^{2}x(t)+e^{-x(t)}$. If I assume $E[x(t)]=0$ the solutions are very easy, for example mean: $E[y(t)]=E[t^{2}x(t)]+E[\lambda e^{-\lambda x(t)}]=t^{2}E[x(t)]+\frac{1}{\lambda}=0+1=1$ I am unsure if I understand Gaussian process behaviour properly.