5. Consider a discrete M.C. on S = {0, 1, 2, ...} whose transition probabilities are defined as follows: p(k, () = P{Y + Z = (} where Y ~ binom(k, p) and Z ~ Pois(A) are independent. Suppose further that Xo ~ Pois(y) (a) What is the distribution of X1? (b) What is the distribution of Xn? (c) Find the limiting distribution of Xn as n -> co, i.e. limn- P(X, = k). (d) Find the stationary distribution of the chain. HINT: moment-generating function method