First, I flip a biased coin once (prob. of head = 0.8). If the result is head, I set p = 0.4; otherwise, I set p = 0.6. Then, using this p, I generate i.i.d. X1, . . . , Xn from Bernoulli(p). (This is the same setting as Games 1 and 2 in Note 4.3.) You do not know the result of the coin flip, and your task is to infer p. (a) (5 pts) Write down the probability distribution of p before seeing X1, . . . , Xn. (I.e., only based on how p would be generated according to the coin flipping procedure.) (b) (5 pts) For any fixed p, write down the likelihood function for X1, . . . , Xn i.i.d. Bernoulli(p). (c) (5 pts) Your answer in (a) can be viewed as the prior distribution of p, and your answer in (b) is the likelihood. Now, derive the posterior distribution on p. (I.e., the distribution of p after seeing the data.) Hint: What are the possible values p can take? The posterior distribution should only have positive probability on these values. (d) (5 pts) What is the posterior probability of p = 0.4