The question is:
Consider a continuous random number with a Gaussian distribution of mean $\mu$ and variance $\sigma$ . The RV is measured from time $t=-\infty$ to $t=\infty$. This time domain signal $x(t)$ is passed through a first order low pass filter with cutoff at fo. What would the statistics of the output be? Would it still be Gaussian? If yes, then what is the new mean and variance?
I am unable to understand where to start with this. Any help is greatly appreciated.