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I apologize in advance if I have missed the right place to ask. I'd be grateful if you could forward me to the right place, if that is the case.

Google didn't help, so maybe someone here can point me in the right direction:

1) "If the input to a LTI system is a Gaussian random process, the output is a Gaussian random process" <- How do we know this?

All I see on the internet is people showing how to compute stochastic parameters (e.g. correlations and SPDs), but I have no idea how would I manage to show or to derive the statistics of the output process.

2) In most cases, people often interchange the expectation operator and time integral (usually when convolution occurs) without saying anything. I was wondering when exactly is that allowed (and when is not), and what conditions need to be met for that to happen.

Thanks in advance.

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# Statistics of random processes passed through an LTI system

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