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White noise has infinite variance, whereas Gaussian random variable must have some finite-variance to exist. How do two disjoint phenomena co-exist?

Help will be highly appreciated.

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  • $\begingroup$ Definitely a duplicate of the question linked to by pichenettes, and, as discussed in the reference cited there, white noise is a fantasy, but a very useful (and for many, a very lucrative) one to have and to hold. $\endgroup$ – Dilip Sarwate Jul 18 '13 at 13:26
  • $\begingroup$ This is not a duplication. This question is about the difference between the "Variance" of White Process vs. the Variance of Random Variable. I vote to reopen as the discussion can and should be interesting. $\endgroup$ – Royi Jun 16 '18 at 19:10