The following model can be used to describe the number of women (moth- ers and daughters) in a given area. The number of mothers is a random variable X E Po(A). Independently of the others, every mother gives birth to a Po(u)-distributed number of daughters. Let Y be the total number of daughters and hence Z = X +Y be the total number of women in the area. (a) Find the generating function of Z. (b) Compute EZ and Var Z.