SECTION B continued B3. Let X1,..., Xn be independently distributed random variables from a Gamma(a, 8) distri- bution with density f(x|a, B) = Baga-expl-BIL BE (0,00), r(a) where I(t) is the Gamma function and E(X) = $. (a) Write down the likelihood and log-likelihood functions for the parameter 0 = (a, B) based on the sample x. (4] (b) Compute the multivariate score function for the model. You can use y(a) for log (a). [4] (c) Derive the Fisher information for the model. [6] (d) Hence find the asymptotic distribution of the MLE. (4] (e) Assuming & = 1 = 3 provide a 95% confidence region in (0, co) for the vector (a, 3)