I am having a hard time solving this problem.

Problem 3: MILE and MAP In this problem, we will nd the maximum likelihood estimator ME) and maximum :1 posterior-i (NIAP) estimator for the mean of a mime-fate normal distribution. For that purpose, [1 X = {1:1, , 13\"} be an identically, independent distributed (iid) sample drawn from a normal distribution with known variance 62 and unknown ,u dened as follows: fowl = gs 1. What is the joint probability distribution P(X|t9) of the sample? 2. What is the maximum likelihood estimation ME) of the parameter In? 3. Let a has a prior Gamma. distribution given by l #R 18 3 PC\") = r(a)3a WhereaandBareuknown. 3. Please write down the objective mction of maximum a posteriori MAP) estimation of the parameter .u. b. Find the posterior and the Bayes Estimator. (1. Estimate an\" that maximizes the objective mction in a) using MAP estimation. [ll] points)