Looking at the defintion of N-th order stationarity,
The only way I see a random process to be 1st order stationary is when all its random variables (any time) have same distribution. Am I correct?
2026-03-27 06:08:24.1774591704
Does first order stationary random process means that all variables in the collection have the same distribution?
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I think I figured it out. The answer is simply yes, this is obvious from the definition above. Now the reason why this was unsetlling for me, is that this property, if satisfies, basically reduces down the entire space of all possible random signals, to just one random process in which the distributions at any time instant are the same. Actually, there's another way to get interesting signals, even when stationaryity is there, that is through dependence between adjacent random variables in the collection. Having distributions that are functions of time is not the only way to get rich set of signals. After all, specifying a random process, is merely mentioning the distributions of time-indexed random variables, but rather, the joint distribution of all of those.