Is Normal normal?

The rumor says that Normal distribution is everything. It will take a long long time to talk about the Normal distribution thoroughly. However, today I will focus on a (seemingly) simple question, as is stated below: If $X$ and $Y$ are univariate Normal random variables, will $X+Y$ also be Normal? What’s your reaction towards this question? Well, at least for me, when I saw it I said “Oh, it’s stupid.

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Yixuan's Blog

Statistics, Programming, and …?