The Mayo Clinic conducted a study of n = 50 patients followed for one year on a new medication and found that 30 patients experienced no adverse side effects (ASE), 12 experienced one ASE, 6 experienced two ASEs and 2 experienced ten ASEs. (1) Derive the pasterior of A for the conjugate Poisson-Gamma model: Y1 , .... Yalx 19 Poisson(A) and A ~ Gamma(a, b) (2) Use the Polsson/gamma model with a = b = 0.01 to study the rate of adverse events. Plot the posterior and give the posterior mean and 95% credible interval