Consider a Bernoulli random variable r with p(x = 1) = 0. Given a dataset D = {r1,...,EN}, assume N1 is the number of trials where r; = 1, No is the number of trials where a; = 0 andN = No + N1 is the total number of trials. Consider the following prior, that believes the experiments is biased: 0.2 if 0 0.6 p(0) = {0.8 if 0 = 0.8 otherwise 1. Write down the likelihood function, i.e., p(D|0). What is the maximum likelihood solution for 0 (we already have derived this in the class)? 2. Consider maximizing the posterior distribution, p(D|0) x p(0), that takes advantage of the prior. What is the MAP estimation?