I'm looking for a proof of Cramer's theorem that states the following:
Let $X,Y$ two independent random variables such that $X+Y$ is normal distributed, then $X$ and $Y$ are normal distributed.
Any help will be appreciated
2026-05-04 10:02:09.1777888929
Cramer's theorem reference request
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You can look at the original paper: Harald Cramér. "Über eine Eigenschaft der normalen Verteilungsfunktion". Mathematische Zeitschrift, 41 (1): 405–414, 1936.