[8 marks] For two positive numbers a, b > 0, let X E N and Y E (0, co) be two random variables whose joint behaviour is described by P ( X = n, Y 0. a) [2 marks] Find the marginal probability mass function of X, i.e., P(X = n) for n = 0, 1, 2, .... (Hint: a Gamma density integrates to 1 over (0, co).) b) [2 marks] Find the conditional density of Y given X = n, and deduce that X +1 E( Y X) = atb c) [2 marks] From P(X = n, Y