Question 5 [8 points] Suppose Y|a~Beta(a, 3) , i.e., the data Y has the Beta(a, 3) distribution with unknown parameter a. The possible values of a are a1 = 2, a2 = 3, and a3 = 4-, and the prior PMF of a is given by g(a1) = 0.4, 90.12) = 0.4, 90.13) = 0.2. Suppose the observed data is Y = 0.5. Find the posterior PMF of a using a Bayesian update table