You are given a coin and a thumbtack and you put Beta priors Beta(100; 100) and Beta(1; 1) on the coin and thumbtack respectively. You perform the following experiment: toss both the thumbtack and the coin 100 times. To your surprise, you get 60 heads and 40 tails for both the coin and the thumbtack. Are the following two statements true or false? _ The MLE estimate of both the coin and the thumbtack is the same but the MAP estimate is not. _ The MAP estimate of the parameter θ (probability of landing heads) for the coin is greater than the MAP estimate of θ for the thumbtack. Explain your answer mathematically.