# independent Poisson-distribution random variable

Let $V,W,Z$ independent Poisson($\lambda$)-distributed random variable. $\lambda>0$. $X:=V+W, Y:=V+Z$

how can i show, that X and Y are independent?

• I would be surprised if they were. If, say, $X=1000$, it makes it less likely that $V=0$, hence that $Y=0$. – Arnaud Mortier May 23 '18 at 22:22
• Dumb question: $X$ and $Y$ both have $V$ in them so probably they aren't independent? Idk. Are there cases where you could have independence in a similar case? – BCLC May 26 '18 at 16:42
