2. The frequency of heavy rains in one week follows a Poisson distribution with parameter A. According the past years, the rate )~ Unif{1,2,3, 4, 5, 6}. In the past 4 weeks, we have observed 4, 6, 5, 3. We want to give a proper estimate of A. Let X denote the frequency of heavy rains in one week. Please answer the following questions. (a) Find the joint probability of the data points 4,6, 5, 3 when A = j. (b) With the observed data points 4,6, 5, 3, please find the conditional distribution of A, p(A\data), subject to a constant. (Hint: p(X\data) x p(data|A)p(A), where p(data|X) is calculated in part (a) and p(X) is uniform on {1,2, 3, 4, 5, 6}.) (c) With the previous results, write a pseudo-code for p(\|data). (Hint: one way is to use the rejection algorithm for the kernel function. You can also identify the exact probabilities and use inverse method or table method.)