Hi, I'm revising for an upcoming test and have a past paper with answers but I can't understand where they are coming from. If anyone could try explaining this too me it would be greatly appreciated.
The number of eggs laid by an insect is a random variable which has a poisson distribution with expectation so for Independently for each egg laid there is probability each that it develops into a male insect or a female insect. Let denote the number of male offspring, and the number of female offspring.
i) Find the joint probability mass function of
ii) Show that the marginal distribution of , the number of male offspring, is Poisson with expectation
The answers I've been given are
i) for non negative intergers
ii)For non-negative integers ,
as the sum is
If anyone can explain how you get to these answers it would be a massive help,