There exists a two dimensional correlated probability distribution which gives $(x,y) \sim D$ such that neither coordinate $x$ nor $y$ are normally distributed, yet their difference $x-y \sim N(0,1)$. What was surprising to me is that the marginal distributions of $x$ and $y$ are the same, and ha...

There exists a two dimensional correlated probability distribution which gives $(x,y) \sim D$ such that neither coordinate $x$ nor $y$ are normally distributed, yet their difference $x-y \sim N(0,1)$. What was surprising to me is that the marginal distributions of $x$ and $y$ are the same, and ha...