Question 13 2 pts Let X1, . .., Xn be iid Poisson ()), and let ) have a gamma (or, B) distribution, the conjugate family for the Poisson. What is the posterior distribution of )? " (XIIt , Xi) = gamma (a + Ili= Xi, ItnB " (NZ, Xi) = gamma (a+ Zi= Xi, Its B " (NIIT , Xi) = gamma (a + IIt=1 Xi, InB " ()EZ, Xi) = gamma (a+ Zi=1 Xi, n8+1 n8Question 14 2 pts Assuming a univariate Gaussian data likelihood given N i.i.d. data points: p(X | M) = [In= 1 N (an | /, 62 ) , and a Gaussian prior distribution on the mean: p(/ | Mo) = N (M | MO, ). Suppose /MLis the ML estimator for /. What is the update equation for MAP estimator given a batch of M data points? O 02 O 02 Mo Mozto2 AML O 02 Moo Nozto2 Ho + No? to2 PML O No2 Nozto2 Po + No2+2 PML