The problem is: Let $X$ and $Y$ be independent Poisson random variables $X\in Po(x+6)$ and $Y\in Po(x^2+6x-20)$. Find that $x$ for which the mean of the random variable $Z=X|X+Y=n$ is $n/2$.
I'm not sure if the condition is only $X$ or it's $(X+Y)$ because there is no brackets and if they mean that $X+Y=n$. I've tried to search for some similar problem but can't find anything.
If someone has an idea how to approach this I'll be very thankful!