I have small 2 questions:
Is the sum of two Poisson variables only then a Poisson variable, if they are independet?
If $X,Y$ are Poisson. And $X=Y$. Is $Z= X-Y$ also Poisson (if they are independet or not)?
2026-04-03 21:10:24.1775250624
Small question about Poisson variables
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Regarding the 2nd question, assuming you didn't mean $X = Y$, you can find the distribution of $X - Y$ here. It is called a Skellam distribution and looks quite complicated.