7. MAP estimation for the Bernoulli Trials with Priors. Consider a Bernoulli random variable x with p(x = 1) = 0. Assume we repeat the Bernoulli trial N times and observe X1, . . ., IN. As discussed in the class, the likelihood function is given by p(X1 = 1, . .., XN = CN) = i) Consider the following prior, that believes the experiments is biased: '0.3 if 0 = 0.1 0.2 if 0 = 0.2 P(0) = 0.2 if 0 = 0.8 0.3 if 0 = 0.9 0 otherwise Derive the MAP estimate under this prior. Discuss how the MAP estimation would change as a function of N