Symmetric sum and symmetric product of two independent random variables
Let X and Y be independent r.v.'s. Then it can happen that X, \(X+Y\) are symmetric while Y is not symmetric. If at least one of X and Y is symmetric then XY is also symmetric. On the other hand, XY can be symmetric even if none of X and Y is symmetric. Other related observations are also discussed.
scientific article; zbMATH DE number 4096479