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Exercise 15.7.4. Take X P = p ~ Binomial(5, p), and now test Ho: p = 1/2 versus HA: p + 1/2. Consider the test that rejects the null hypothesis when X 6 {0,5}. (a) Find the size a of this test. (b) Consider the prior distribution where PHol = P[HA] = 1/2, and P| HA ~ Uniform(0,1) (where p = 1/2 is removed from the uniform, with no ill effects). Find P[X = x | Hol, P(X = x | HA], and the Bayes factor, Bag. (c) Find P[Ho | X = x]. When x = 0 or 5, is the posterior probability of the null hypothesis close to a