The random variables X and Y are defined in terms of the random variable N which is Poisson (lamda): X is Binomial (N, p) and Y = N - X. Show that X and Y are independent, and find their distributions.
I think we should consider the joint mement generating function in order to prove X and Y are independent, but I get stuck on getting the joint memnt generating funcion.
Anyone got any clue?
... and the ones that won't