2. The probability that a certain coin shows Heads when flipped is unknown. You model this parameter as a random variable with a beta prior distribution with (hyper) parameters a = 2 and B = 2. You flip the coin 18 times and observe 13 Heads. a) Find the posterior distribution for 0, the probability of Heads. b) Compute 0, a posterior Bayes estimate for 0. c) Conduct a Bayesian test of the following hypotheses: Ho : 0 E [0.5, 0.7] versus Ha : 0 # [0.5, 0.7] d) Write a 90% credible interval for 0