Deriving statistics of band limited Random Noise

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 $f_o$. 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.

• This is a badly posed question. If it really is homework (that is, the OP is merely copying what has been asked, and not his/her understanding or translation of what has been asked), then the instructor deserves censure. Unfortunately, the accepted answer is even worse. Commented Aug 30, 2017 at 14:37
• Actually it is homework. I was hoping for some leads. Do u have any? Commented Aug 30, 2017 at 14:38
• @ dilip Actually professor I was hoping you would take a look at this. I have seen some of your answers on similar questions where people have asked to generate band limited noise and your lecture notes appendix on white noise. This was actually a discussion in class. What information do you think is needed and how should we proceed with this? Commented Aug 30, 2017 at 15:05
• @ dilip-sarwate i'm open to any feedback to improve my answers. I guess using random variable instead of random process is the problem. I tried to write the answer using random process concept, but then i taught it's not a common knowledge (even for some so called experts in the field) so i changed it to random variable, but at the end i give a hint that we must use random process. Commented Aug 30, 2017 at 16:36
• I've made some correction to my answer. Commented Aug 30, 2017 at 17:46