1. Suppose conditioning on A = A, Y m PoissonUi] and A has a gamma distribution with mean E[i't) = n 2 an and coefcient of variation tar139. (a) Showr that the unconditional mean and variance for Y are E{Y] = p, = new and Var(Y} = on + 0:21;. [b] Note that A has the density function mime} = nip} (2):) exp (2) a for A :> D. Show that the marginal distribution of Y has the probability mass function fY[yia1V} : fory:,1,2,.... [-3) Show that if L! is known, the distribution of Y has the exponential family form with variance function V01] 2 n+n2/y. (Hint: dispersion parameter =1J [(1] Note that if L! is unknown, the distribution of 1" does not have the expo- nential family form. Show that if 131 = to I le1 for some parameters 50,9, the variance function is VLU) = Var') = ,u + 9p + wig. Use this meanwvariance relationship to nd the quasilikelihood for it based on a single data point 1