I know that the sum of two normally distributed random variables is also normal.
But what about the opposite? Can the sum (or substraction) of two non-normally distributed random variables be normal?
X-Y=Z Can Z be normal if X and Y are not? Any example?
I came to this question while thinking about the need of checking normallity of the differences of paired measures.
The question Is joint normality a necessary condition for the sum of normal random variables to be normal? is not the same than mine, it speaks about joint normallity.
And this one Sum of independent non-normal random variables says it's a duplicate but I can't find the original one.