4.2 Tumor count comparisons: Reconsider the tumor count data in Exercise 3.3: a) For the prior distribution given in part a) of that exercise, obtain Pr(θB < θA|yA, yB) via Monte Carlo sampling. b) For a range of values of n0, obtain Pr(θB < θA|yA, yB) for θA ∼ gamma(120, 10) and θB ∼ gamma(12×n0, n0). Describe how sensitive the conclusions about the event {θB < θA} are to the prior distribution on θB. c) Repeat parts a) and b), replacing the event {θB < θA} with the event {Y˜B < Y˜A}, where Y˜A and Y˜B are samples from the posterior predictive distribution.