12. Let XJp"' Binomial(10, p). Consider the two models: 1 1 M0 : p = 2 versus M1 : p :f. 2.

Under M1 , consider the following three priors for p: (i) U(O, 1), (ii) Beta(10, 10), and (iii) Beta(100, 10). If four observations, x = 0, 3, 5, 7, and 10 are available, compute kd given in Equation (6.27) for each observation, and for each of the priors and check which of the observations may be considered outliers under M0 .