Suppose that the number of fish in a big sea $A$ adheres to a Poisson distribution. What is joint probability mass function of having $x$ male and $y$ female fish?
I thought that I could just divide A by $\frac{1}{2}$ and add the two together... but that didn't make very much sense on second thought...:
$ M \rightarrow \text{ the number of male fish.} \\ F \rightarrow \text{ the number of female fish.} \\ P(M = x, Y = y) = 2\frac{e^{-a}a^{x+y}}{2(x+y!)} $