Final Exam Question 2: Instead of flipping a coin, let's assume we spin it on the edge of a table. In this scenario, where the edge is not perfectly even, the probability of landing heads (9) is not exactly 1/2 but is specified to be either 1/3 or 3/4. When the coin is spun on its edge n times, the number of heads observed (y) follows a binomial distribution ( y ~ Bin(n, 0)). The prior distribution for the probability of heads (e) is assumed to be a mixture of two beta distributions: (0) = Be(10, 20) + Be(20, 10) B(a,b) represents the probability density function of a beta 0-1 (1-0)6-1 Here, Be(a, b) = (a)(b) distribution with parameters a and b, and B (a, b) : = T(a+b) (a) Find the posterior distribution p(ely). (b) Calculate the posterior mean E(0|y).